While heating a plate, the coil-side of it is cooler. Why is that?

The coil is a water-cooled piece of copper, so the area around the coil is close to water temperature.

There could be two reasons. The coil is a water-cooled piece of copper, so the area around the coil is close to water temperature. Consequently the coil provides the cooling in this respect, so you can see a measured difference in temperature in between sides. You may actually be having some interference on the coil side from the magnetic field if that side is reading cooler which may be creating the issue. So I’d look at these two factors to figure out what may be contributing to the temperature mismatch.