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LISA Pathfinder (LPF) was a technology pioneering mission designed to testkey technologies required for gravitational wave detection in space. In the lowfrequency regime (milli-Hertz and below), where space-based gravitational waveobservatories will operate, temperature fluctuations play a crucial role sincethey can couple into the interferometric measurement and the test masses'free-fall accuracy in many ways. A dedicated temperature measurement subsystem,with noise levels in 10$\,\mu$K$\,$Hz$^{-1/2}$ down to $1\,$mHz was part of thediagnostics unit on board LPF. In this paper we report on the temperaturemeasurements throughout mission operations, characterize the thermalenvironment, estimate transfer functions between different locations and reporttemperature stability (and its time evolution) at frequencies as low as10$\,\mu$Hz, where typically values around $1\,$K$\,$Hz$^{-1/2}$ were measured.

Temperature stability in the sub-milliHertz band with LISA Pathfinder