The difficulties with the theory of core warming are many. For one we have little knowledge as to how the magma will behave relative to the iron core(both molten and solid.) The actual dynamics of the heat release is at this point a mystery. Yet it seems reasonable to assume that besides the emission of infra-red radiation(which will itself be hampered by certain conditions at the sub-surface level, or even by greenhouse gasses at the surface) and convection currents which will develop as relatively stable steady-state core temperature stabalizers, there will also be unusual bursts of heat due to the chemical makeup of the substances at the core. Therefore you will expect sudden elevations in thermodynamic activity. These “explosions” if you will are likely very slow to happen, perhaps thousands of years, but they will add to the difficulty in detecting the existence of a cyclical pattern of temperature variations in the core.
It is also true that a solid Iron core at very high pressure will conduct heat at a much greater effeciency than a liquid Iron core at less pressure, and both of these will conduct thermal energy much more effeciently than the magma layer. (It is also true that the Iron core, solid should conduct electricity better than the molten core.) Therefore there exists an expectation in variations in the effeciency of thermal conduction from the core to the surface. While most heat is probably created at the core, and likely sent up to the surface, it is likely impeded by conditions at the sub-surface and surface and at the various layers. This dynamic in itself is going to cause variations in volcanic activity.
There is good reason to believe that the Earth is actually cycling through alternate periods of warming and cooling at the core itself, and that these variations are largely responsible for the long period variations we see in the surface climate. Let us assume a steady state between the energy released from the core and the energy created within the core. Though we cannot be certain as to exactly how this energy is facilitated, that is how it is distributed over time, or for that matter how it is created since the theory of nuclear material, or tidal friction, or else the possibility of an orbital pressure caused by the uneven acceleration towards the sun are all theories that are little understood, and seemingly not grounded on indisputable foundations. At least this can be said of the nuclear theory, and the last theory of orbital acceleration. As for friction caused by the tides of the moon, this is pretty well understood and is a phenomenon which is not disputed. However, even in the case of this mechanism, we really do not know the details of how exactly the resulting energy would be distributed. For example how much energy is released as the deeper fluid of the core is subjected to tidal forces that travel along what is a presumed solid iron core? We have very little understanding of the behavior of iron under tidal stress at the enormous pressures and temperatures at the core. It would be very difficult to calculate exactly how much energy is actually released due to this phenomenon because of these pressures and temperatures.
It is true also that even the solar radiation absorbed by the Earth’s lithosphere is difficult to calculate due to the inexact knowledge we have of the lithosphere: it’ s geometry, and it’s chemical makeup. The temperature and pressure of the magma just below the lithosphere remains a mystery as well. Even if we really knew these parameters, we would likely not know what kind of variations exist just below the surface. However, the only certainty is that there are variations.
For all this it can be shown that the Earth’s core must vary in temperature if in fact we have a steady state thermodynamic equillibrium between the energy in and energy out. If we assume that the sub-surface of the Earth absorbs whatever energy is supplied to it either from the Sun, or from the tidal friction or from nuclear decay or from orbital accelaration and that ultimately this energy distribution is ubiqutious throughout all the sub-surface region of the Earth: that is to say that ultimately this heat energy must warm all the areas of the subsurface(to different degrees of course), then we can prove that the Earth’s core temperature must vary.
When we say the distribution of heat energy is ubiqutious we are not saying that everywhere the heat energy is the same, we are nearly certain that it is much hotter towards the center of the Earth than at the surface regions, or near the surface regions. There is also very good reason to assume that the greater amount of heat is actually created at the core since the tidal friction at the core is likely to be much much greater than nearer to the surface. We know also that much nuclear material is likely to be at or near the core, such as uranium, or irridium or radium. Certainly it would seem plausible that much of this material would be located deep within the Earth, otherwise it would have been at the surface. Why is it not? Where therefore is all this material deposited by comets and asteroids for billions of years? It must be assumed that it is located deep within the Earth nearer the core. Whether pressure and temperature might actually play a significant role in the disintegration of these elements is also left to future experiments.
As for the existence of a heat source due to orbital perturbations, though not proven, if it were true, it would likely be greater at the core than the surface, since the pressure at the core is far greater and therefore much more massive than at the surface, thus we have a far greater heat source.
In general whatever else the heat sources may be besides rotational friction it is true that as the Earth’s interior layers heat up, they will also expand. That is to say as they absorb this heat they will expand. As the expansion occurs, some increase in pressure will also occur for some interval of time. Therefore the solid iron core and liquid iron core will both experience a pressure increase as the temperature increases if even for a short period of time. Since this temperature increase will not be immidiately relieved by radiation or convection which would lead to eruption, there will be a temporary wave of heat energy which will increase the pressure on the iron core and the liquid core. However as this temporary pressure wave passes through the core, it will also increase the temperature. As the temperature is increased however at the iron core, the core itself will have a tendency to liquify especially at the boundary levels where the iron core meets the liquid core. Thus the iron core will expand, and as it expands will further release heat as the molecular bonds are broken. Now the tendency will be for the heat to travel outwards towards the cooler regions as described roughly by the fourier principles, that is the heat will radiate outwardly, and the overall pressure on the core will actually lessen since the exapansion will radiate towards a larger volume towards the surface of the Earth. However, as this pressure drops at the core, the core temperature will also drop which will prompt the liquid core to solidify again at the boundary levels. But as it solidifies it will again release heat energy which starts the process all over again. Therefore we have an oscillating expansion and contraction of the core.
This expansion and contraction at the core will ultimately have implications at the surface. This excess heat and pressure would have to be released at the surface. As the inner material of the Earth is exposed to the surface environment a cooling will take place and thus excess heat at the sub surface regions is expunged and a cooling will take place.