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The aim of the present work is to better understand the gravitational drag forces, i.e. dynamical friction, acting on massive objects moving through a self-interacting Bose-Einstein condensate, also known as a superfluid, at finite temperatures. This is relevant for light scalar models of dark matter with weak self-interactions that require nonzero temperatures, or that have been heated inside galaxies. We derived expressions for dynamical friction using linear perturbation theory, and compared these to numerical simulations in which nonlinear effects are included. After testing the linear result, it was applied to the Fornax dwarf spheroidal galaxy, and two of its gravitationally bound globular clusters. Dwarf spheroidals are well-suited for indirectly probing properties of dark matter, and so by estimating the rate at which these globular clusters are expected to sink into their host halo due to dynamical friction, we inferred limits on the superfluid dark matter parameter space. The dynamical friction in a finite-temperature superfluid is found to behave very similarly to the zero-temperature limit, even when the thermal contributions are large. However, when a critical velocity for the superfluid flow is included, the friction force can transition from the zero-temperature value to the value in a conventional fluid. Increasing the mass of the perturbing object induces a similar transition to when lowering the critical velocity. When applied to two of Fornax's globular clusters, we find that the parameter space preferred in the literature for a zero-temperature superfluid yields decay times that are in agreement with observations. However, the present work suggests that increasing the temperature, which is expected to change the preferred parameter space, may lead to very small decay times, and therefore pose a problem for finite-temperature superfluid models of dark matter.