I say if you want it there...put it there! Yea, sometimes the easy "slam dunk" answer is to just say NO you can't do it that way or whatever because of the heat, etc. so that's why you're on this forum and you're asking questions, so keep asking. In some of these applications you then have to think about how might "customize" somethinnnng, and I dunno what that is yet, yea could be receeding it into the wall like suggested, not sure, but keep thinking and asking until something starts to work? I also like to look at the asthetics of the TV and don't like all the cords hanging or showing and I like it too look real sharp, just me I know, but I'm not alone. So, WHEN I do put my TV above the stove, I'll have all the cords (power, hdmi, etc., ) behind the wall and in chase, just like you see in many a bar or restaurant, so I'd say to keep that in mind. I see many a blower on a lot of beautiful stoves here and then the first thing my eye see's is that ugly power cord...EWE, but again, it's what you see that's important.
Also, sometimes the room ergonomics just don't work that well and maybe everything is built to have the tv and entertainment center in one certain location and unless some renovation is in the works then you may be limited. Or could be room windows and glare situations too. There are now wireless options for connectivity as well. Yea, wireless hdmi but it's ~ $900 so kinda outta my budget at this time, but all you need then power. Best of luck!
Also, sometimes the room ergonomics just don't work that well and maybe everything is built to have the tv and entertainment center in one certain location and unless some renovation is in the works then you may be limited. Or could be room windows and glare situations too. There are now wireless options for connectivity as well. Yea, wireless hdmi but it's ~ $900 so kinda outta my budget at this time, but all you need then power. Best of luck!