I've been using this amp for years Mono Bridged. Using it Mono-Bridged, in my mind is not making the amp work harder, it letting it work with more headroom by using the 2 power amps inside, instead of pushing one amp harder. Regardless, I don't know which way generates more heat. As for pushing air "into" a case with your amp, you may be making the cooling effectiveness worse. The internal fan in the amp case is trying to push hot air "out".....so if you use fans, set them so you are sucking air out and not blowing air in.
Anyway, when I was using that amp in a hot rehearsal space, cranked up; I would use it out of the case, which makes that amp easy to transport, and the best way to let it vent.