If the size of the penny was reduced to just a few atoms, wouldn't changing the number of atoms in the penny affect the rate at which the penny itself could emi

If the size of the penny was reduced to just a few atoms, wouldn't changing the number of atoms in the penny affect the rate at which the penny itself could emit radiation through blackbody emission? If so, I would expect there would be a size at which the penny could be small enough that it's temperature could grow arbitrarily large once the heat flux in = heat flux out from the penny.