Wire your remote turn on wire to the control of a relay (typical automotive relay, aka Bosch relay, will work fine). For a Bosch relay that's terminal 85. Ground terminal 86. Run constant +12V (for instance from your distribution block or your amps +12V terminal) to terminal 30. Attach terminal 87 to your amps remote turn on and also to + wire of fans. Ground the negative wire of the fans.

If it's a small enclosed area (like amp mounted under plexi or similar), you're better of with all fans pushing or pulling air at one end, and a passive vent at the other end, instead of pushing in air at one end and pulling out at the other.

/Michael