The expansion of the conductors is the least of your problems.
The real issue is the effect of excessive temperature on the insulators. The plastic in the cable has three electrical functions:
- To insulate the two separate conductors.
- To provide a specific constant dielectric between the conductors. This is necessary to make the transmission line impedance fixed and predictable.
- To hold the conductors at a fixed geometry relative to each other. This is also necessary to make the transmission line impedance fixed and predictable.
The cable is rated to a maximum temperature for a reason. The manufacturer isn't guaranteeing the cable's properties above 80°C, which probably means they know the plastic will start to loose necessary properties above that point. Most likely the impedance will suffer first as the dielectric constant changes. At a bit higher temperature, the mechanical properties of the plastic change to the point where the conductors might touch, resulting in a short.
Your question really comes down to "What happens when the maximum ratings are violated?". I think you already know the answer.
In this case it seems that unreliable operation of the crane not only has significant economic cost, but also serious safety problems. You really need to get this fixed now! A planned shutdown for a few hours is way better than a crane with a pot of molten steel suddenly having a mind of its own in the middle of a production run.
One advantage is that your transmitter and receiver can be fairly close to each other, so you should get good signal to noise ratio with relatively low power. You probably also have some distance before the signal gets off the premises where anyone else would care.
There must be a better place to put the antenna that doesn't require running 80°C coax right above molten steel. Where are the transceiver electronics now? Those must be in a cooler place. Why can't the antenna be near there, with maybe only a metal whip sticking out that can take much higher temperatures than polyurethane? With good placement of the fixed transceiver, there should be enough coupling even with less than optimal moving antenna placement.
As for the magnetic fields from the electric heaters, that should not be too much of an issue. The frequency should be much lower than whatever you are using for communication. Also, one of the advantages of coax cable is that all external magnetic and electric fields are common mode. Between the very different frequency and the fact that the interference is common mode, the external magnetic fields should not be that hard to deal with.
they poked a hole in the cabinet and placed the antenna outside, connected with an ordinary RG58
Why not have only a metal whip antenna poking out of the cabinet? Maybe the cabinet location is not optimal for an antenna, but maybe you can compensate by clever placement of the other antenna. Between that, the right frequency, the right power level, and the right protocol, this really should be doable. It sounds like your data rates are very low, which should also allow for better overall signal to noise ratio.
Looking back I'm confused now about which antenna is moving. I originally thought the problem was getting data to/from the moving crane, but you say the electronics are in a cabinet. Is the problem that the operator is moving around? If so, surely that could be dealt with by putting the fixed antenna and electronics in a cool part of the room.