Amps that don’t impersonate space heaters.

Go Class D, Atma, Hypex, Purifi, ADG. I don't think you would be sorry.

The Buckeye 1ET9040BA is barely warm to the touch and has the accuracy, insight and musicality I had hoped for. Very low SNR so not to intrude on your high sensitivity speakers.

Otherwise maybe a First Watt?

You're lowest heat, yet still awesome option is a nice simple SET.  You don't need muc power but any class A SS amp will have more watts than you need and all the heat associated with them.  

Your BAT uses the 6C33C tube that is one of the hottest ones out there.  It runs about twice the temperature and radiated heat goes as Texp4 so the increased tempeatrure adds a lot of radiated heat.  Also the BAT makes much more power than you need.  A imple 300B or 2A3 amp will be less heat than a TV screen, perhaps 100 watts (heat, not sound). Your BAT is likely 3-400 watts.  

An even lower power option is the Decware SE84series which is about 50 watts and plenty of power to drive those speakers.

Jerry

@helomech interesting. 
My Wilson Sabrinas are 87db and dip into 2ohm. 
I have 2 amps - CSIB and Boulder 866. Different bass but the Coda isn’t lacking. I’m slightly puzzled by your findings but it could be room and speakers. My system is in a pretty small room - 15x13

I started using class D am[lifiers in my space-constrained home office a few years ago.Earlier this year I picked up cherry, 4 yr-old pair of Bel Canto 600M monoblocks. I can't say enough good things about these amps.They have a smooth, refined, powerful sound. They're a real taste of the high end. And of course they put out very little heat.

I do the AGD Audions for the summer and switch to Primaluna mono blocks for the winter. I look at it as a space heater that sounds great!