  We derive the stochastic master equations which describe the evolution of
open quantum systems in contact with a heat bath and undergoing indirect
measurements. These equations are obtained as a limit of a quantum repeated
measurement model where we consider a small system in contact with an infinite
chain at positive temperature. At zero temperature it is well-known that one
obtains stochastic differential equations of jump-diffusion type. At strictly
positive temperature, we show that only pure diffusion type equations are
relevant.
