Solid State Low powered Amplifiers

Like a few others have recommended in the above posts, the First Watt amps would be a good fit for you and the Klipsch speakers.  I use the First Watt F8 with my Volti Razz and am very satisfied with the synergy.  My F8 runs warm but is not hot to the touch..... also live in the south! 

The First Watt J2 I had in my system sounded quite good--not really like a good low-powered tube amp, but good nonetheless.  However, it ran fairly hot, so I don't know if would help your room situation.

Bakoon amplifiers are Class A/B cool running and sound fantastic.Especially with high sensitivity speakers.They sound better than the vast majority of SETs and Class A SS amps.

I feel like I have left out a recommendation of a Low Powered SS Power Amp' that has thoroughly impressed me during demo's in a variety of Build Models, which I made known recollection of experiences had on this forum.

 The Neurochrome Modul 65 has been in use in my Local HiFi Club as a SS Amp' demonstrator for quite a few years. This Amp' had been used in comparisons to both Valve Power Amp's - Valve Integrated Amp's and the same in SS.

It has been used driving Quad ESL's both Vintage and Modern, as well as much kinder loads for a Speaker.

Where it really showed it strengths, was at a time when it proved quite difficult to separate its presentation qualities during a comparison to a EAR 899 Power Amp.

With the resident 899 in the system used, the system Value is close to £50K

With the Modul 65, the system Value is closer to £40K

Neurochrome Amp's are today my top of the list consideration for Amp's when I retire from using my system that is totally Valve Orientated. 

FYI, In a £200K System with a Soulution Power Amplification and a value of approx' £150ish K with the Neurochrome Modul 686 as the comparison Power Amp', the system was just as impressive with the 686 included, some from the short term demo' received made their preference for the 686 known. The system owner was usually an outspoken individual, which following the demo' was not too outspoken,       

I’d recommend the Schiit Aegir.  I use one with Devore Nines and it’s an excellent amp.  They are about $500 on the used market so fairly low cost just to try out. Good luck with your search.