Upon adding the potatoes to the oil, the temperature drops precipitously, then comes back up, but you should limit how far back up it comes.

As they finish, potato chips are not very massive and contain little residual water, so the oil temperature could easily go way over 400 degrees, even on my antique stove.

This is not so much a problem with the French Fries, as they also go in at 400 Degrees, but are done by time the oil gets back to 360 or so because they are much more massive and contain a lot more water.