For 3L, you can power all your channels.
As you want to primarily drive LCR, you could consider a 5 channel power amplifier that has bridgeable support so that you could club two channels and get additional power for your Klipsch front stage.
There are primary things that you should consider while choosing the power amplifier. They are,
- RMS watts per channel (Higher the better)
- Transformer design (condenser / toroidal). This would be class A, B, AB, D, etc.,
- Damping factor (Higher the better say 200 and above)
- Filter capacitance (Higher the better)
These combinations make a lot of difference in the overall sound quality. The better the value, the better the dynamics.
There is a difference in the sound quality and dynamics; also from my personal experience, the power amplifier offloads the AVR amp section
(to whichever channel is given in pre-out) due to which there is a considerable amount of heat reduction in the AVR. It won't run hotter but it will run warm.
Any power amplifier would run warn or hot which you can control it by placing a laptop cooler on top. It will run the power amplifiers cool
(not even warm).
Please do some research and understand the aforementioned points and choose a power amplifier wisely!