We show that a single imperfect fluid can be used as a source to obtain a mass-varying black hole in an expanding universe. This approach generalizes the well-known McVittie spacetime, by allowing the mass to vary thanks to a novel mechanism based on the presence of a temperature gradient. This fully dynamical solution, which does not require phantom fields or fine-tuning, is a step forward in a new direction in <?format ?>the study of systems whose local gravitational attraction is coupled to the expansion of the universe. <?format ?>We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity.