It should be,
kTg=qgεg∗rg
where kTg is in Joules per particle, and qgεg∗rg is potential (J) due to temperature charges on one particle.
Only if one started somewhere somehow, anywhere anyhow...
Tk=r∗TTg
where r=qgεgkΔT or
Tk=rg∗TΔT
where rg=qgεgkTg

(T_k\) is made up of TΔT up to the length rg of a field projected by the total temperature charge per particle, up to a potential of V=kTg. Where Tg is the temperature of the gas when the temperature particles it contains, fill the gas evenly at a volume of Vm, radius r=3. T is the measured temperature at the surface, and ΔT is the difference between the measured temperature T and Tg.
If the temperature charge particles are free from the gas particles, T=Tg where the measured temperature is the same as the temperature of the gas just below the inner surface of the containment. T is independent of Tk.
If the temperature charge particles are bounded to the gas particles and moves to the interior of the gas as the gas particles moves, then T≠Tg and Tk is related as above.
At high temperature and high pressure it is likely that T is independent of Tk as more temperature particles are free from the gas particle. Tg then measures the temperature charge content of the gas, as in the case of a conductor imbued with electric charges.
Tg≡ρeareaε=D
Have a nice day.