Currently, I do not have any knowledge of finite temperature field theory. But I have learnt ordinary QFT calculations and I am reasonably familiar with Statistical mechanics. With this background, I wonder if there is a simple way to get the basic idea of the following scenario.
Consider a $T=0$ QED process. To be specific, let me consider the $e^-e^-\to e^-e^-$ scattering. I know how to calculate the scattering amplitude of this process at tree-level. There are also corrections at one-loop, two-loop etc. Now, let us imagine the same process supposing that this system of photons and electrons are now in equilibrium in a thermal environment.
Why does the scattering amplitude of the same process at $T\neq 0$ differ (or get modified) from $T=0$, physically?
What is the concept or what is the physics distinguishes this scattering process at $T=0$ from $T\neq 0$?
Please let me know if I have communicated the question well enough. As I do not have a fair knowledge of this, the question might be unclear.