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To measure the temperature of a macroscopic scale requires a relatively long timescale (I would guess on the order of seconds for a regular thermometer), so the system probably reaches thermal equilibrium between the atoms and electrons (perhaps on the order of nanoseconds) before a temperature measurement can be obtained, so I think that your question isn’t really relevant. If you could get an instantaneous temperature, you’d have to get into the atomic-scale physics of how your thermometer works. How is heat transferred from your work-piece to you thermometer? Through the electrons on the atoms?
Another way to examine this problem is to think about the definition of temperature if given the particle information:
T = ( sum_over_particles (mass_particle * velocity_particle ^ 2 ) ) / (3* number_of_particles * Boltzmann)
The free electrons can be considered to be independent particles and their small mass will weight the temperature calculation accordingly.
Paul