This would be a great place for a real NYC fireman to step in and tell us how & where the recording of the radio transmissions is usually handled. I'm tempted to guess that the recording setup is in a truck or van (remembering all the crushed vehicles at the periphery of the site), and that the vehicle might have protected the equipment to some extent. I don't see how it could have survived if it had been inside either of the towers or inside #7. Tape melts pretty easily.
I'm not FDNY, but I'm pretty sure those recordings were made on machines within the towers themselves. Due to all that steel and concrete, the Department's walkie-talkie radios (which tend to suck even under perfect conditions) didn't have the power to reach outside the building on their own. So a number of repeaters (with recorders built in somewhere along the line) were installed inside 1 & 2 WTC themselves every X number of floors up, which allowed transmissions from outside to penetrate in all the way to the 110th floor, and vice versa. But something happened at some point (crash damage or something) that caused the repeaters to stop working, at least above a certain number of floors. So the firemen above a certain level could only communicate with each other, not anyone below or outside, but the tape kept rolling.
As for the potential of tape melting, I believe the recorders were put in "black boxes" at least as strong as those in your average Boeing, if not more so.