I second the cutting large holes into the bottom of the cabinet for airflow. (Unless the bottom is pretty well sealed all around. (if it is open in the back at the floor , the bottom holes will still help. (A bunch of 2" holes would be great..)
If you have the right sort of ventilation, you may not need a fan.
The BP-26 and power supply really will be pretty good with minimal ventilation (holes under shelf, and above back should do OK..
The amp however will need some serious thinking to make it cool fan free, Maybe no shelf under amp chassis.. just rails.. feet fit on. Then big opening to rear behind. So air freely flows from below fins up and the out above amp back...
Computer parts (like 'New Egg') has a device to control fans via temps.. Used for computer cases.. could be used for your amp fan.. i would use one to minimize fan noise..
Even if you use a 120VAC fan, a motor type dimmer could be used to slow it down for that perfect noise/ performance point.
As for remote? some companies make a repeater.. a discrete box sits on top. wire to repeater at infrared eye of equipment