I have been wondering about it all day as I heard that particles of bodies at absolute zero have no kinetic energy. So, is it true that the total kinetic energy of an ideal gas is equal to its thermal energy?
Absolutely not except in the case of an ideal, classical, monatomic gas, with no further degrees of freedom.
A counter-example would be a completely degenerate gas. The degenerate particles have a range of non-zero kinetic energies, right up to the Fermi energy, but none of this can be extracted as heat. The ideal degenerate gas therefore has zero thermal energy and much less thermal than kinetic energy even when not completely degenerate.
For an ideal classical, monatomic gas, all of the kinetic energy can be extracted as heat and indeed the thermal energy and kinetic energy are the same. However, if you start thinking about classical gases of molecules then there may be further degrees of rotational and oscillatory freedom that also store thermal energy, so the translational kinetic energy and thermal energy are not equivalent.
In short, yes. Although in thermal physics it is often more useful to define "internal energy" of a system (rather than thermal energy) as being the sum of both kinetic and potential energies of the constituent particles, since separating the kinetic and potential components can be difficult.