Heat in class A equipment

It depends entirely on how well the amplifier is ventilated. Heat also will work its way from the heatsinks through the chassis so over time the entire amp will get warmer.

If it’s designed well, it should live a long heathy life. Depending on the power supply sizing, load, etc..  they can get quite warm too. As do some resistors. 
keep the dust off parts and the vents unobstructed, should be all you need to do.

I have a preamp that gets real toasty when the tubes are on. Most of the heat is from The power supply and rectification. Tube side of the chassis is cooler actually. I looked up the specs for the transformer to see what the operating temperature range was. While the unit gets very warm, it’s nowhere near the limit specified for the transformers max temperature range. 

Heat in some of the older class-a designs radiates throughout the entire chassis, thus impacting all parts inside. 

The old class-a solid state theory of leaving the amps "on all the time", comes at a price. Had to scrap some great amps "for parts" where certain boards and pieces inside could not be fixed or rare parts inside were not available any longer. Argh.  

Some of my current mono tube amplifiers run much cooler than former designs, and thankful to designers for re-thinking how to make things last longer too.      

I have Class A amps from Pass Labs rated for 200 watts; they're big, they're bad-ass and they're happening!  All jokes aside, I don't concern myself with that (meaning heat), because it is what it is.  First and foremost, I bought these puppies for their sound, and they make my Von Schweikert VR-6 floor standers sing like nothing else.  Ehh, what I'm driving at is just take the good with the bad, because everything in life has some sort of compromise.  For me, it must make my speakers sing, and sing they do so that makes me content.  Anyways, I wish you happy trails on your OCD hunt for heat off your amps...  Hah!