It shouldn't be much at all. Since the luminosity of the Sun is P = 384.6e24W, the perpendicular solar irradiance at 1AU is I = P/(4*pi*AU²) = 1.368e3W/m². I've calculated
here that the Earth's thermally radiates about 8.39e16W, while the total incident power at an albedo of a 0.306 is 5.34e16W, i.e., a significant fraction of the Earth's heat is generated internally, while a quick websearch shows that the Moon's tidal forces slow down the Earth's rotation on the order of centimeters per century (figures varied, but they were all in this range; trying to sort them out as to which is accurate is uninteresting, so I'll skip that). Treating this as torque on a sphere of Earth's mass, this represents a power drain (τ⋅ω) of order 1e12W, which must be compensated for in some way. This is really an upper bound, and is still much less than the 1e16W order that should be generated internally. As to Io, it also has other moons with which to play.
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