Good eyes, clutchc!
OP, the fan speed changes you describe on start-up are normal.
What usually happens (with a properly working system) is this:
1. On start-up, the fan automatic control system sends the fan the full 12 VDC to ensure it starts up properly.
2. After most of the POST process is finished (less than 30 sec, maybe only 5 to 10) the automatic control system gets a valid reading from the CPU temp sensor, which is cool - the unit has been off. So the fan speed slows down to match the measured CPU temp.
3. As you use the system and the CPU heats up, the fan speed rises and then changes up and down as the CPU load changes.
MAYBE your brother was wrong. If he did not realize how badly the heatsink was clogged, just as you did not, he may have come to the wrong conclusion, too. See how it all works when you get it cleaned, fitted with new thermal paste and reassembled properly.