The peculiarities of a high value, low cost, amp

Bought the acclaimed STA200, last year. 

Was surprised to find it can drive my Tekton Moabs with fully developed, detailed, musical sound. I've practically passed out in front of my Moabs, time after time, late at night, for the past six weeks, starting when they first entered my home.

When I push the volume into dynamics that persist into the 85db and up range, for the better part of an hour, the amp yields a fair amount of heat to the top of the chassis and the rear heat fins. This is concerning. Things start getting hot and I draw the volume down. I imagine I'm not the only one facing unseasonable heat with their amps... I keep my tuning mostly to jazz and acoustic sections. Occasionally, I get an itch for rock and roll or something that pushes the bass down and deep. A week ago, I played Lorde's "Royals" and could hear the amp struggle to push the bass notes out, full and clear. There just wasn't enough juice. This, of course, nudges me away from bass rich electronic content, somewhat regrettably, as I do love to embrace as much variety as comes my way.

Another piece, is that the STA is stated to NOT work (well?) with 4ohm speakers, and that is probably what is happening in my description of the limits of the higher volume and bass (electronic) heavy content. Now, I mostly keep my listening in the 85db and under range, and the music is gorgeous. I can hardly believe I'm riding on Moabs, a $500 amp, and a few other inexpensive pieces that collectively deliver sound that I never though I would be able to afford.

Still, the amp is running at its limit on the "bigger" bass pieces. I keep specifying electronic bass, but I'm sure there is more that would push the amp into heat mode. To be more precise, it is probably when deep bass notes are pulling 90+db that the amp fails to keep up, and what is a deep electronic bass note if you can't feel it, thick and full.

So, I'm curious as to your thoughts on what I'm running into... is the heat a problem? I hear it's damaging... If this amp is one of the "steals," but I'm running, on occasion, to its limits, what other "steals" are out there?

When I say steal, I think of things like what I'm reading about class D audio amps. For all of $600 or $700 I can bring an amp into my home that provides 400-600 watts per channel, accommodating the 4ohm load of the speakers... 

The Schiit aegir looks very attractive, but I don't think I will have more than 40 watts a channel and then the problem with Royals.

The Vidar looks interesting, could surely push the drivers more effectively than the STA, but I hear the highs are a bit forward and I want my highs right where they are - clear, pure, authentic, not at all harsh.

There may be some other interesting options, but keep in mind - I want very high value for my dollar. Used might be an option...