  We consider a quantum system coupled to environment at a fixed temperature
and describe the reduced evolution of the system by means of a Redfield
equation with effective time-dependent contact temperature obeying a universal
law. At early times, after the system and environment start in a product state,
the effective contact temperature appears to be much higher, yet eventually it
settles down towards the true environment value. In this way, we obtain a
method which includes non-Markovian effects and can be further applied to
various types of GKSL equations, beyond the secular approximation and
time-averaging methods. We derive the theory from first principles and discuss
its application using a simple example of a single quantum dot.
