A DHC8-400's #3 HYD PUMP light illuminate after departure from the gate. The aircraft returned to the gate.

Narrative

I was boarding up for a flight when Inspector from the FAA showed up to do an en-route. I briefed him on his duties; he read the briefing card and we were ready to pushback. After completing my departure brief I asked my First Officer and Inspector if they had any questions or anything they would like to add. The Inspector noted that the right fuel temperature was showing red (about 73 degrees). I informed him that was because the fuel/oil heat exchanger was not operating due to the fact the engine was not running. I also ensured him that as soon as the engine was started the fuel would be well within my air carrier operating limitation (0-71 for continuous operations). He did say the use of the aux pumps to cool the fuel temps is just a temporary fix to a bigger problem. Just like we talked about; I started engine two at the gate using the GPU and the fuel temperature instantly went to 65 degrees. After starting number one and completing the pushback I had the First Officer run the 'after start checklist.' Unfortunately the '#3 HYD PUMP' light illuminated. I had my First Officer run the checklist; which directed us return to the gate for maintenance. Inspector said nothing more than he was going to call it a day. After watching me write the #3 HYD PUMP up in the maintenance logbook; we shook hands and he went on his way.