Technically it would, but the same way an individual ant's breath contribute to global warming.
Note that the thermal energy contained in the inner earth isn't a fixed amount: the earth constantly generates new heat from friction and radioactivity, and that new heat is radiated away in space at night, alone the heat captured from the sun during the day. So technically geothermal will increase the efficiency of this heat transfer a tiny bit, but it's really a negligible amount. (In reality the ant's contribution to global warming is probably orders of magnitude than the phenomenon we're talking about here).
Note that the thermal energy contained in the inner earth isn't a fixed amount: the earth constantly generates new heat from friction and radioactivity, and that new heat is radiated away in space at night, alone the heat captured from the sun during the day. So technically geothermal will increase the efficiency of this heat transfer a tiny bit, but it's really a negligible amount. (In reality the ant's contribution to global warming is probably orders of magnitude than the phenomenon we're talking about here).