[Physics] Why are only infrared rays classified as “heat rays”

Question

I've often heard that Infrared rays are called "heat rays". However, I feel like this term is a misnomer. Don't all the wavelengths of electromagnetic radiation carry energy?

Judging by how gamma rays are highly penetrating and are dangerous when absorbed by tissues, radiations of lower wavelengths should carry more energy, and should be able to increase the internal energy of the object that absorbed it much more than infrared rays can. This seems consistent with the conservation of energy for an isolated system: $$T_{ER} = \Delta E_{int}$$
where $T_{ER}$ stands for transfer of energy by electromagnetic radiation

Then why are UV rays, X-rays and gamma rays not classified as "heat rays".

Answer 1

Infrared region is a part of electromagnetic spectrum that is mostly responsible for the radiative heat transfer in our everyday life. It is expressed by the fact that the peak of the Planck distribution at room temperature lies in the infrared range:

Planck radiation has a maximum intensity at a wavelength that depends on the temperature of the body. For example, at room temperature (~300 K), a body emits thermal radiation that is mostly infrared and invisible. At higher temperatures the amount of infrared radiation increases and can be felt as heat, and more visible radiation is emitted so the body glows visibly red. At higher temperatures, the body is bright yellow or blue-white and emits significant amounts of short wavelength radiation, including ultraviolet and even x-rays. The surface of the sun (~6000 K) emits large amounts of both infrared and ultraviolet radiation; its emission is peaked in the visible spectrum.

Electromagnetic waves with frequencies a bit higher than infrared are visible light. Therefore, although they also carry heat, they are mainly identified with the information that we get through our eyes.

Lower frequency electromagnetic waves, in radio spectrum, are less energetic and therefore less important.

Clarification
In thermodynamics/statistical mechanics heat is the energy transferred from one system to another on the microscopic level (unlike work, which is due to macroscopic changes). In this case an object is in contact with radiation. Heat rays is not a physics term, it should not be literally interpreted as "rays carrying heat". But the reason why we use this term to describe infrared radiation is the one that I give above.

Comment on the energy conservation
The radiative energy absorbed depends not only on the energy of photons of given frequency, $h\nu$, but also on the number of photons, $n_\nu$, i.e., the absorbed energy at a given frequency is $$E_\nu=n_{\nu}h\nu.$$ If we assume thermal distribution for $n_\nu$ and do calculation, we obtain the above-mentioned Planck formula. This is why the peak of the Planck formula corresponds to the ferquencies where the most heat is transferred.