A hypothetical time-variation of the gravitational constant G would cause neutron star matter to depart from beta equilibrium, due to the changing hydrostatic equilibrium. This forces non-equilibrium beta processes to occur, which release energy that is invested partly in neutrino emission and partly in heating the stellar interior. 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

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... g reactions. Comparing the surface temperature of the nearest millisecond pulsar, PSR J0437-4715, inferred from ultraviolet observations, with our predicted stationary temperature, we estimate two upper limits for this variation: (1) |Ġ/G| < 2 × 10^-10 yr^-1, if we allow direct Urca reactions operating in the neutron star core, and (2) |Ġ/G| < 4 × 10^-12 yr^-1, considering only modified Urca reactions. Both results are competitive with those obtained by other methods, with (2) being among the most restrictive.