Why is EGT decreasing on a jet engine when the generators cut in (take over)? Is the EGT decrease related to the generators cutting in or is it related to the fact that the fan is now providing enough ventilation air for the engine?

When I say cut in I mean that the engine driven generator has taken over in supplying the electrical load from the APU driven generator.
EGT on some engines is proportional to the engine developed power, cutting the generators reduces the needed power, thus reduces the EGT