Temperature... Feels Hot

From the post "Add By Subtracting..." dated 23 May 2016,

$\cfrac{pV}{T}=-\cfrac{T^{+}}{\tau_o}.\cfrac{V}{A_o}=-\cfrac{T^{+}}{\tau_o}.\cfrac{1}{2}\cfrac{rh}{r+h}$

the problem with this expression is that the variation of $\cfrac{pV}{T}$ is dependent on the geometry of the experimental setup from which $\cfrac{V}{A_o}$ is derived.  In this case, a volume confined in a cylinder of base $2\pi r$ and variable height $h$.

This aside, from the same post above,

$p_d=T_E=\cfrac{\rho_{\small{T}}}{\tau_o}=T_n.T_{Ep}$

$T_{Ep}=\cfrac{T^{-}}{A_o\tau_o}$

due to the distribution of $T_n$ on the inner surface of the containment, could be the temperature that we commonly measure.  This distribution of $T_n$ particles on the side the containment or any body in thermal contact with another body of unequal temperature potential is the result of a flow of temperature particles.  Flow stops when,

$p_{d1}=p_{d2}$

$T_{n1}.T_{Ep1}=T_{n2}.T_{Ep2}$

where it is possible that $T_{n1}\ne T_{n2}$ and $T_{Ep1}\ne T_{Ep2}$

This is different from electric potential difference that drive the electric current across similar conductor.

This explanation allows for two bodies of different materials in thermal contact to have different temperatures, but no temperature particles flow between them.  One body is insulating the other hot body.

$T_{Ep}$ is specific to a material and depended on the material lattice, $\tau$ a material constant and the availability of $T^{-}$, $T_n$ inside the material.

This at last is temperature.

Note:  If $p_{d1}=p_{d2}$ is the case, then it is possible to push temperature particles from an insulator to a body and have the latter attain a higher temperature.