All Class-A amplifier transistors are hot to touch, otherwise it's not Class-A anymore, right?

Now depends what the idle current would be and how the heat from the output transistors is dissipating to the case, so what Class-A headamp do you own and you're referring to, please?
For HPA-3B & 3U the case itself it's part of the heatsink, so it will be quite warm to hot to the touch after a couple of hours of operation and I mean at least 50C during summer. Power required from main would be around 15W when idling and even more when headphones connected and driven.
More about this here:
http://www.head-fi.org/t/770610/introducing-the-matrix-m-stage-hpa-3u-and-hpa-3b-review-to-follow/60#post_12178996
http://www.head-fi.org/t/770610/introducing-the-matrix-m-stage-hpa-3u-and-hpa-3b-review-to-follow/105#post_12397517
http://www.head-fi.org/t/770610/introducing-the-matrix-m-stage-hpa-3u-and-hpa-3b-review-to-follow/60#post_12157815
As you can see, I had lowered voltage from 36V to 30V, so I can use other op-amps; this also means internal temperature decreased a bit, so now it's less than 50C (I can do a measurement tonight again if you like).