How hot is too hot?

Several decades audio repair, and can tell almost instantly whether unit on 24/7 or shut off when not in use.
The heat cooks the components (which are designed for heat to a point) AND the solder, which in units made after 2006 will be Lead-free solder and does poorly in high heat cycle environments.
My experience the solder joints will fail before most components.

Turn it off when not listening, solid state warms up very quickly. I get home and fire up the stereo and it's ready for listening within 15 minutes.
My 3 cents (inflation)

Turn it off when not listening, solid state warms up very quickly. I get home and fire up the stereo and it's ready for listening within 15 minutes.

wise advice imo

or use the standby mode if the unit has one

What you have to consider is the Hint has a HT Bypass which would mean though control functions are relinquished the Hint is still operational if you are running your mains throught the Hint when in HT. Most people leave their TV on all day if not listening to 2 channel, therefore it would be on all day as well. I'm not sure why yours would be hot. Honestly mine never gets more than a bit warm. 

When it's to hot to touch...