Just shows how little you know about the laws of Physics, Johann.

Mars is not COLD, in any absolute sense. Compared to interstellar space, Mars is quite warm. Everything radiates energy away, at frequencies and rates predictable from its temperature and the nature of its surface.

A theoretical "black body" radiates with a characteristic (log-normal) pattern of energy whose amplitude and frequency both increase with temperature. As a consequence, the total radiated energy is proportional to the 4th power of the absolute temperature - this is the Stefan-Boltzman law.

Interstellar space is not at absolute zero. Instead, it radiates at the characteristic 2.7 K temperature of the echo of the big bang.

An isolated planet in interstellar space would equilibrate to 2.7 K, modified slightly by any internal heat production (whether by radioactive decay, chemical differentiation, or ongoing compaction).

A body in orbit around a star intercepts solar radiation proportional to the area it presents to that star. For a spherical planet this is simply pi * R^2. More properly, the shape is an oblate spheroid of rotation, plus higher order shape factors, but these are only tiny modifiers. The received radiation per unit surface diminishes as 1/D^2 where D is the orbital distance in AU.

Earth orbits at 1AU, where the received energy of all solar radiation is 1560 W/m^2 (Watts per square metre). Earth would have a mean surface temperature of 260 K, if it were a naked rock in space with a neutral spectrum (i.e. a "black body"). The greenhouse effect on Earth is worth ~25 K to yield a total average global temperature of 285 K.

Mars is at 1.524 AU, and its solar radiation scales as 1/1.524^2 i.e. 43% of the energy received by Earth = 671 W/m^2

The equilibrium temperature scales (by the S-B law) as energy^1/4, so Tmars=Tearth*43%^0.25 = 210 K. The greenhouse effect on Mars is only worth a few K, yielding a mean of 213 K. Every square metre of Mars radiates, on average 1/4 of the energy received by the notional planetary disk - 168 W/m^2, so Mars is far from "cold".

If the planet rotates, it shares the heat on all faces, but some parts get more on average. For low spin axis inclination, the equator gets more energy and the poles less, so the poles are cold, on average, and the equator warm.

Seasonality increases with inclination, so the poles of a highly inclined undergo huge seasonal variations, yet are warmer on average than a non-inclined planet since they are sometimes warm, and the cold they see in mid-winter is no worse than the winter of a less-inclined pole (the radiation to space is never to a black body colder than 2.7 K).

At very high inclination (> 55 degrees), the seasonally averaged polar temperature is actually warmer than the equatorial!

For planets with thick atmospheres and oceans, temperatures are partially equalised by fluid convection.

Now, to your stupid misunderstanding:

Although individual photons of high energy radiation may be vastly more energetic than lower energy radiation, like visible light and IR, the number of them emitted by a black body is many many orders of magnitude less than the photons of visible and IR radiation, so the contribution to temperature from High energy radiation and also from Cosmic rays is infinitesimal.

As an example of this, medical X-rays do not lead to measurable heating of the target.

And so it is with earth and Mars. The high energy radiation to Earth above the ozone layer and to Mars' surface is enough to be biologically damaging, but it offers no appreciable warmth.

Trust me, the levels of atomic radiation required to make things physically warm (such as the conditions inside a working nuclear reactor), are so many orders of magnitude worse than the surface of Mars or earth that it is clear that your mental abberation in associating the two is pathological.

I have no more to say to you on this or other issues.

learn, or leave.