Also, if it scales like that you're probably better off using the Kelvin scale. If you are looking for something down that alley, however, may I recommend the whip becoming incredibly cold at times. This does place limits on the cooldown time, as it is literally impossible to go below absolute zero, and if you also have to make sure the whip does not break under the stress caused by sudden temperature changes, it would add a unique element to their strategy.
Say you are working with 20 degrees Celsius (room temperature) being the "resting temperature", and its temperature can be regulated by a "points" system (This is just to explain the logic, I cant think of any better way to describe it.
if it can go to 520 Celsius for 30 seconds (just using your numbers here), let's assume its maximum point threshold is 500*30=15,000 points. If one wanted to recharge the heat in battle, they could have a brief cooldown at which it returns to resting so as not to crack, then chills to -230 Celsius (44 degrees Kelvin, 250 "points" per second of cooldown). It would have to be like this for a minute to completely return to a resting state, but during this time it has to be held as a sword (otherwise it would crack way to easily), and then the heat functionality would be restored.