Lagrange Equation for thermal system

I am working on modeling of a multi-physical system using Lagrange based modeling and we know that Lagrange function, $L$, can be defined as below;
$L= T-V$
where:
$T=$Kinetic Energy
$V=$Potential Energy

Now my query is how to define Kinetic energy and potential energy for a thermal system in terms of $T$ and $V$, so one can put it into Lagrange function and also how to define generalized forces in the thermal system for Lagrange equation.