In reality this is almost a meaningless question since "temperature" is simply not a well defined parameter at low temperatures (and strictly speaking temperature is not defined at all below 0.65K since this is the lowest point that is defined on the international temperature scale ITS-90, but that is another issue).
I am of course not saying that you can't use the concept of concept of temperature at low temperatures. But one there is no single, well, defined parameter "T" any more.
A good example is solid state systems where the temperature of the electrons is usually higher than the temperature of the lattice (the phonons); since the interaction times become so long at low T they can differ by several hundred mK.
(As far as I remember the electon-phonon
interaction time actually goes to infinity as temperature goes to zero, meaning you will never reach a true thermodynamic equilibrium).
There are also plenty of room for confusion due to the fact that temperature is also often used as a measure of energy.
When people talk about laser-cooled gases the temperature they refer to is in reality the "kinetic" temperature, i.e essentially the kinetic energy of the particles divided by Boltzmann's constant. However, the statistics of the gas is not given by a classical distribution so this is not a "true" thermodynamic temperature; it is just a measure of the average velocity of a (small) group of atoms.
In some research fields people also talk about the "temperature" of radiation, this is only a "real" temperature if the radiation is coming from a black body but the word is still used even when this is not true; e.g. for a monochromatic source the "temperature" is just
Also, the original meaning of the word "temperature" in statistical mechanics is only meaningful for ensembles; a single particle or small collection of particles can't (according to this definition) have a "temperature" which means that you can't -strictly speaking- talk about the temperature of e.g. ions in an ion trap.