Is the maximum rated current of the cable the same for any voltage?
The heating you get in a wire is only dependent on the current you pass through it.  The voltage makes no difference.

But you need to check the voltage rating of the cable you are using.  For Ethernet cables, it can be very low.  A random cable I just looked at is only marked 30V (which was rather surprising since power-over-Ethernet is nominally 48V).

If you are pushing a cable to its limits, then where it is run can also make a difference.  A cable enclosed in insulation can get rather hot, while one in free air cools a lot better.  Don't exceed the temperature rating of the cable.  Again, the random cable I have to hand is only rated for 60°C.