I am looking for examples of instances or families of quantum channels that arise out of an interaction of a quantum system with an environment having some temperature. For instance, the generalized amplitude damping channel (of Nielsen and Chuang, Sec. 8.3.5) can be modelled as a unitary interaction \begin{equation} \begin{pmatrix} 1&0&0&0\\ 0&\sqrt{1-\gamma}&\sqrt{\gamma}&0\\ 0&-\sqrt{\gamma}&\sqrt{1-\gamma}&0\\ 0&0&0&1 \end{pmatrix} \end{equation} between a system and an environment in a thermal state $(1-e^{-\beta})|0\rangle\langle 0| + e^{-\beta}(1-e^{-\beta})|1\rangle\langle 1|$, followed by discarding the environment.
I am especially interested in channels that experimentalists would use to model plausible temperature-dependent interactions in existing implementations of qubits.