  We present a new method to detect Fermi surface instabilities for interacting
systems at finite temperature. We first apply it to a list of cases studied
previously, recovering already known results in a very economic way, and
obtaining most of the information on the phase diagram analytically. As an
example, in the continuum limit we obtain the critical temperature as an
implicit function of the magnetic field and the chemical potential
$T_c(\mu,h)$. By applying the method to a model proposed to describe reentrant
behavior in $Sr_3Ru_2O_7$, we reproduce the phase diagram obtained
experimentally and show the presence of a non-Fermi Liquid region at
temperatures above the nematic phase.
