What model receiver is it, in particular? Sometimes (with quite old models) the surround channels would be underpowered, compared to the mains (L/C/R) - this would limit how loud you could play it (check for matching power ratings of front & rear channels in the manual). 'Heat up' is very subjective, I really can't answer that - the most comfortable I would be with running an amp for extended periods would be hot enough so that I could touch the heatsink & not feel like I'm being burned (just below pain threshold). How that translates into what you feel atop the case is anyones guess...
When you said the impedances match - if the subwoofer is in the lowest range that the receiver can support, it will produce more heat than if it were driving a higher impedance (although the hotter amp will also be delivering more power into the load, so using a lower impedance speaker is equivalent to increasing the volume by 3dB).
Running a surround channel for this poses no problem, in all likelihood it's identical to the other 5 channels (at least for modern receivers), although bass-content tends to benefit more (in transients) from more power, which is why using a receiver for this may make for a weaker performance. If the sub is in the lower impedance range of the receiver, you can parallel-bridge the surrounds channels. Basically, you tie the inputs together (same source for both surrounds), and tie the output positives together at the woofer - this way, each channel will be (effectively) driving double the impedance of the woofer, which will reduce heating. Parallel bridging, however requires both surrounds channels to be level matched (exactly), or else bad things could happen (or perhaps just some protection activates, no way for me to know).