Hmm, that is quite hot the 70 C / 80 C, I mean). Is it in a restricted place, with little or poor ventilation? That is a power amp, and by definition it produces (well, better say it can produce) heat... The fact that the temperature tends to rise with time of use suggests me exactly what I said... four fingers in every dimension is the minimum IMHO. the more the better.
How have you placed your amp(s)? Some people like to hide them inside lowboards to make the setup more “wife-friendly”, which would not work well with the F10. We are currently experiencing a heatwave here in Central/Western EU, and after a few hours of operation the temperature still remains below 50°C (2× F10, bridged, 23 dB; measurement taken on the left side, directly in the centre of the cooling fins). Give them enough space to breathe; they are not particularly efficient, considering that each unit already consumes 90 watts at idle. In the image, you can see the two amps; the temperature difference between them is 2K simply because the lower one has slightly less circulating air.
These days, in the south-west of the state of Hesse, 50°N, outside 42°C inside up to 32°C, the amps going up to 57°C, i would also say that arround +3k are their participation to the room climate if not even more.
I have a Mark Levinson No 534 with no fan. It runs in class A for most normal listening. Sounds really good even without turning the volume up. It runs very hot and is a larger case than the F10. I had to place on an amp stand to allow plenty of heat dissipation. Most high end amps don’t have a fan since they make noise. I had one years ago and it never even activated since I lived in an apartment and couldn’t play it real loud.
57°C under worst case scenario temperature here is not bad. I don't expect arround 40°C outside every week in summer here, at least not this year.