I own a BAT VK-33SE preamp and VK-255SE power amp. My speakers are 88 Db efficiency. The amp drives them effortlessly, with plenty of safe headroom, and I find it to sound it's best after about 30 to 45 minutes. It gets quite warm by 30 minutes, maybe you could say hot, but never a room heater. BAT products work very well with one another. They are designed and engineered to do so. The VK-255SE amp is one of the most "tube-like" sounding solid state amps available. Since you have a BAT Rex-2 preamp it would be a very good decision to match it with a BAT power amp. That's one suggestion. Another suggestion is to get a BAT tube amp. The Rex-2 power amp (as well as the Rex-2 preamp) have both been recently replaced with the next-generation Rex-3 products. Thus, the Rex-2 power amp can likely be had at a nice discount. You may wish to contact Upscale Audio about that. They have a Rex-2 power amp set up as a demo unit. It is only switched on when a demonstration is requested. I visit the store fairly often and can tell you that amp is in absolute perfect condition. Upscale Audio is a wonderful retailer to do business with. I am confident they would work a nice price for you on that unit. Anyway, I thought you may want to take into consideration pairing your preamp with the engineered mate of power amp and also provide you with a very good path for such opportunity.
Best of luck to you.