Why a room below the surface (such as basements) can stay cold all the time? How is it able to avoid the high increase of temperature and heat in hot days and periods?
[Physics] Why basements stay cold even during summer
temperaturethermodynamics
Related Solutions
Addressing only the question of "Will the Earth grow cold?", the fate of the universe turns on cosmological considerations.
Short answer: Yes.
Slightly longer answer: By measuring the thermal gradient of the crust in deep caves and boreholes at many places on the continental and oceanic crust it is possible to find an approximation to total geothermal power.
Aside: A substantial portion of the geothermal flux in this era is from radioactive decay rather than from gravitational potential.
Results published (the link is the the arXiv preprint, but the paper also appeared in Phys. Rev. B) by the Borexino collaboration in 2010 and by the KamLAND collaboration in 2011 (Nature Geoscience) are consistent with roughly half of the geothermal power of the Earth being due to radiological decay.
These measurements also put strict upper limits on the power of a theorized natural nuclear reactor at the core (the data are now consistent with zero reactor power).
Both Borexino and KamLAND are large anti-neutrino detectors and are directly sensitive to the anti-neutrino emissions of radioactive beta decays such as those found in the Uranium and Thorium chains (but not to Potasium-40 on account of using inverse beta decay as the detection mechanism). From this data we can reconstruct the overall radioactive decay activity in the deep Earth, and compute the total power represented.
Disclaimer: I worked on KamLAND for 3 years, but am not named as an author on the paper cited herein.
Further disclaimer: much of the text here is adapted from my earlier answer on Skeptics.SE.
It's pretty much as you say. But it sounds as though you're trying to guess. I'd suggest a couple of little sketches and some first principles reasoning; see my drawing below
Both the circles are my reversible heat engine. On the left, it is running "forwards" and yielding work $W$ from the nett flow $Q_C$ into the cold reservoir at temperature $T_C$ after extracting heat $Q_H$ from the hot reservoir at temperature $T_C$. On the right it has work $W$ done on it for a nett flow nett flow $Q_C$ out from the cold reservoir, and the total $Q_H=Q+Q_C$ is pumped into the hot reservoir. By definition of the thermodynamic temperature in terms of heat flow ratios in reversible heat engines, as I discuss in my answer here, then
$$\frac{Q_H}{T_H}=\frac{Q_C}{T_C}\tag{1}$$
and, by energy balance
$$Q_H = W+Q_C\tag{2}$$
The engine is reversible, so that all the magnitudes of the energy quantities are the same; their signs are opposite: instead of the heat engine doing work $W=Q_H-Q_C$, we must do work on the heat engine to pump $Q_C$ from the cold reservoir and thereafter dump the total energy $Q_H=W+Q_C$ back into the hot reservoir.
So you now work out both efficiencies from (1) and (2): for the heat pump, a sensible "efficiency" is the fraction of the heat drawn from the hot reservoir that we convert into work; from (1) and (2) it is:
$$\eta = 1-\frac{T_C}{T_H}$$
For a heat pump, a sensible definition of "efficiency" is how much heat $Q_C$ we draw out of the cold reservoir for input of unit work: this ratio is:
$$\frac{Q_C}{W} = \frac{Q_C}{Q_H-Q_C} = \frac{T_C}{T_H-T_C}$$
although this one is a bit weird insofar that it can be greater than 1. Note that it becomes infinite as $T_C\to T_H$: heat can move spontaneously without work input between two reservoirs of the same temperature (although for a finite reservoir, the flow would lead to a temperature difference and halt the flow). A better word, which I believe heat pump engineers use is "co-efficient of performance": the bigger it is, the less energy you need to put in to remove unit heat from the cold reservoir.
Best Answer
Dirt is an exceptionally good insulator. As seasons change, the temperature of dirt 5-10ft underground changes a lot less than the temperature of the air. The deeper you go, the less the change. So, in the summer a basement will be "cool" because the ground surrounding it is cool (relative to outside temperatures), and in the winter it will be "warm" because the ground surrounding it is warm (relative to outside temperatures), despite "cool" and "warm" both being the same temperature (probably about 50-60F if you're in the southern USA).