To start with , elementary particles that decay, as the muon, have a random decay according to the decay curve of the quantum mecahnical calculation at the center of mass of the muon. When moving with high velocities the decay time changes following special relativity. So in this sense, if you could have a gas of muons (experimentally not possible due to its small lifetime) there would be a very tiny difference in the average lifetime at the two temperatures samples , because the individual particles have an internal "clock".
On a gas composed out of particles that do not decay,as your example of He, there is no measure of "age" for the individual atom, so there can be no change in the age of the gas. If radioactive atoms are used in the gas as for example iodine131, a difference would be found between the two temperatures in the lifetime of the sample, as iodine should decay slower in the hotter sample, and the Xenon content as a function of time would be measurable.
Atoms that are used for atomic clocks, do have a complicated individual timer.
The accuracy of an atomic clock depends on two factors. The first factor is temperature of the sample atoms—colder atoms move much more slowly, allowing longer probe times. The second factor is the frequency and intrinsic width of the electronic transition. Higher frequencies and narrow lines increase the precision.
From this talk which discusses gravitational red shift Atomic clocks versus atomic gravimeters I would expect that the answer would be yes, that temperature will have an effect on the measured timing of the clocks ( which is not exactly a decay or aging but an interesting effect).
The indiviual atoms/molecules have to have an internal "clock" for the whole sample to be "aging" faster , at 0 K.