A more detailed explanation of the temperature "support" mechanism is required because an objection is often raised that the net outward heat flow from the core is far too small to warm the atmosphere. Indeed that is the case, but over the course of even the last billion years there has been ample time for it to do so, especially with the aid of the Sun.
It may help to picture the whole distance from the liquid core to the top of the mesosphere, that is, the mesopause. We have no control over that relatively fixed distance, nor over the liquid core temperature (maybe averaging about 5,400 deg.C.) Nor can we control the mesopause temperature which is known to be about -100 deg.C. There is a (negative) temperature gradient from the core to the surface and then a negative gradient from the surface to the tropopause, then a positive one to the stratopause and a negative one to the mesopause (Above that the thermosphere can be much hotter than the surface, but it contains relatively few molecules and has no effect on anything below.) Hence there will be a natural equilibrium temperature at the surface (in the absence of solar radiation at night) as the heat passes through the surface/atmosphere interface. So we can say this temperature is "supported" by the heat flow.
Now, we do not have accurate measurements of core heat at various latitudes, but we do have hundreds of boreholes which provide data at depths around 300 to 500 metres. So we can "pick up the plot" at those depths, which are well beyond the influence of solar heat, and we can extrapolate the trend to the surface. Over the life of the Earth, the surface temperature in any location has been "set" by the mean Solar radiative flux entering the atmosphere above, together with the adiabatic lapse rate which is a function of the mass of the atmosphere and the force of gravity. The sub-surface temperature plot then adjusted to meet the surface at the temperature found there. Underground temperatures now play a stabilising role, so no major change in climate is possible in a short period.
When the temperature plot gets very close to the surface (perhaps 30 metres underground) it may meet up with incoming heat from the Sun. The plot will then have a trough at that point and there will, in effect, be a pool of "temporary" extra heat that flows in from the Sun but then flows out again during the late afternoon and night.
Now, if we only consider borehole data at somewhat deeper levels than that trough, we find that the temperature plot is "aiming for" a temperature at the surface which turns out to be very close to what we will call the "stable base temperature" which is (approximately) the temperature we would measure just above the surface perhaps an hour or so before sunrise on a calm mid-winter night.
The fact that this happens shows that, over the course of millions of years, the temperature plot adjusts so that it is an approximately linear one from the core to the surface. This is what happens with conduction: the temperatures at each end determine the gradient due to a feedback mechanism.
It is probably not difficult to envisage why the water near the floor of the ocean is at about the same temperature as is found in the crust just under the floor, because we are all familiar with heating water on a stove. Heat is transferred by conduction (sometimes called diffusion) from the stove (or the crust) to the water and an equilibrium state is achieved.
However, on land we get a more direct and immediate effect from the Sun, and so there is a tendency to assume that the Sun does all the warming and the surface has nothing to do with it. But, in fact, heat can also transfer from the solid surface (let's say a rock platform) to the adjacent air by the process of diffusion. But there is very little net heat coming out of the surface compared with that coming from the Sun. Notice, however, that I said "net" heat. In fact, every day (in which the Sun shines) a considerable amount of heat from the Sun flows into that rock surface, and then back out again by night. The net difference is very small, but the total amount of heat transfer each way is quite significant, so the rock can become quite warm. This total heat flow is sufficient to establish an equilibrium so that, as we do observe in calm conditions, the temperature of the first few millimetres of the air is very similar to that of the rock surface. Notice that the heat energy has come almost entirely from the sun.
Now, if cold winds from the nearest pole cool the air at night below the stable base temperature, then when the Sun rises it can more easily warm the air near the surface by temporarily warming the rock a little with heat that then flows back to some molecules in the adjacent air. But when the air temperature reaches that of the surface, some of the Sun's heat enters more deeply and stays in the surface perhaps for most of the day. This slows down the rate of warming of the air. Then, when the heat starts to flow out late that afternoon and night it will only do so until the temperature of the surface cools back down to the stable base temperature, because the temperature trend line for the trickle of heat from the core will still determine the minimum "break out" temperature at the surface. Note that it is possible for some build up of heat during summer months (especially in the ocean) but that will usually dissipate by winter.
And so, just as that same heat flow supports much higher temperatures on the way out from the core, so it will support the surface temperature.
Over the course of many years it is perfectly feasible that core temperatures could vary a little. Some heat comes from radioactive decay and some is thought to come from nuclear fission, which could vary, whilst a portion of the heat generated comes from friction caused by "tides" in the liquid core which are "stirred up" by the Moon, just like ocean tides. There are also solid Earth tides in the outer crust. It is of course gravity from the Moon which does this, and it creates more friction near the Equator than at the Poles because of the spinning motion of the Earth and the fact that the Moon is circling the Earth. Variations in solar insolation (due to different angles) are the main influence on the temperatures at the poles. The solar insolation reaching the surface is reduced by the amount of ozone, but that amount can vary due to solar winds which themselves tend to vary in natural cycles. Likewise, variations in cloud cover alter the albedo.
What reasons can there be for variations in core heat? Marginal variations in total gravity which result from gravity coming from the planets could well provide an explanation. Yes the effect of gravity from, say, Jupiter is very small compared with the Moon. But the compounding effect over many revolutions of the Earth can be sufficient to cause about 3 degrees more or less than the Moon's more constant contribution. See my site earth-climate.com for more detail on climate cycles and possible explanations for such.