  In this paper we study a class of physical systems that combine a finite
number of mechanical and thermodynamic observables. We call them finite
dimensional thermo-mechanical systems. We introduce these systems by means of
simple examples. The evolution equations of the involved observables are
obtained in each example by using, essentially, the Newton's law and the First
Law of Thermodynamics only. We show that such equations are similar to those
defining certain mechanical systems with higher order constraints. Moreover, we
show that all of the given examples can be described in a variational formalism
in terms of second order constrained systems.
