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A hypothetical time-variation of the gravitational constant G would make neutron stars expand or contract, so the matter in their interiors would depart from beta equilibrium. This induces non-equilibrium weak reactions, which release energy that is invested partly in neutrino emission and partly in internal heating. Eventually, the star arrives at a stationary state in which the temperature remains nearly constant, as the forcing through the change of G is balanced by the ongoing reactions. Using the surface temperature of the nearest millisecond pulsar (PSR J0437−4715) inferred from ultraviolet observations and results from theoretical modelling of the thermal evolution, we estimate two upper limits for this variation: (1) |Ġ/G| < 2× 10−10 yr−1, if the fast, “direct Urca” reactions are allowed, and (2) |Ġ/G| < 4 × 10−12 yr−1, considering only the slower, “modified Urca” reactions. The latter is among the most restrictive upper limits obtained by other methods.