I want to know how does the Higgs potential $V(\Phi,T)$ varies with temperature in the Standard model. But I'm not familiar with the finite temperature calculation of effective potential. Therefore, as a starter, I want to learn, how does the potential vary with temperature in a simple field theory such as $\phi^4-$theory. Which references/papers/books should I look at to learn this calculation in detail? I would prefer a simple theory to start with.
If possible, can someone list the steps to be followed in such a calculation?