I've actually been there and done this back in the 80's, it was a 3 man job, even back then, mind, it was us that decided we wanted a safety man outside and would not do it without!
You cannot do if for more than 5 minutes.
You need to be covered up to protect yourself from the heat.
Which makes you get hot quicker IYKWIM.
You can't go in @ 80 deg, you simply can't breathe, we tried!
If it is close to the door, and you can hold your breath you might get away with it, we would do this for jammed hangers.
If the chain came off, we would shut the burners down and leave the fans running as many doors open as we could manage then it would be down to us to decide when we went in and came out.
Even back then, the official line was that it should be cooled down totally.
We would do it on our terms, and often got a job and finish out of it.
No one got hurt, luckily, but, we all were a close knit team, who really watched out for each other.
If you are getting regular chains coming off then you really need to look at the mechanics and plan a down shift, or out of hours works to find out why.
Wear, in the chain, sprockets, or bearings, misalignment due to the bearings failing, or the chain sagging due to stretch or wear, creep due to the materials continually operating at elevated temperatures, thus loosing their tensile properties due to the thermal effects, and physically stretching, or overloading were the normal reasons our chains started detaching themselves from the sprockets.
Normally because we had a run to failure maintenance policy as we were so short staffed no PPM's were done.
IF, we had less breakdowns, by luck, we would go on to PPM's and there was a noticeable increase in plant reliability, then of course we would have a major, that would soak up all our resources, no PPM's so reliability fell again.
If this is new kit, and this is happening already, then lord help you when it gets a bit of real wear & use!
HTH.