No. It's called thermal conductivity. The HS'ses can take heat out of your ship - but in order to get heat out of the FSD, you'll first have to transport it from the FSD to the HS.
The limit is not how fast you can get the heat out of the ship, the limit is how fast you can get the heat out of the FSD, which I imagine as comparatively small, and heating up close to self destruction with every major jump. What would make sense, though, would be jump range (or fuel consumption) dependent charging and cooldown periods. So a 30 ly jump would take longer to charge and cool down than a 2 ly jump.