noooo....you don't want your fan powered down when your heat tape is. You want your fan always going.
Get yourself a computer fan and some type of AC adapter...I have one running off of a cell phone charger and another off of something for a computer component. Cut the wires open and splice them together, cover with electrical tape.
The only thing you have to watch out for is to make sure the adapter is rated roughly the same as the fans.
JonV