Of course there are a number of alternative equally possible answers (well perhaps not exactly equally possible):
Likely scenarios
Teacher heated the far side (before arrival of students) with a blow-torch, soldering-iron, heat-gun or whatever. Then the outside could be above local ambient temperature and be warmer than be inside.
Teacher cooled the near side with ice, cold-spray, rapidly evaporable liquid or whatever. Then the inside could be below ambient and hence colder than the outside.
The plate is coated with a thin coating with highly variable thermal conductivity (or the plate itself has highly variable thermal conductivity) - with conductivity varying from high (outside section) to low (inside section). Then the inside could be warmer (or equi-temperature) relative to outside, but would be perceived as colder by touch.
Inside could be cooled by a draft of cold air, or (more likely) outside is heated by warm air current rising from the lower section of the stove that bypasses the inside section.
The large 10 kA AC cable that runs through the wall of the class-room is inductively heating the outer part of the electrically conductive plate.
Less likely scenarios
Plate is manufactured from plutonium alloy with higher plutonium concentration at the outside.
There is a powerful microwave or infrared beam aimed at the outside, (or for that matter a beam of neutrons, alpha particles, etc doing a similar job).
The students have been hypnotized, or the teacher has manipulated their expectations to the extent that they all 'perceive' or believe the outside to be warmer. Or similarly they live in a totalitarian state and know to keep their mouths shut if reality appears to conflict with state-provided dogma.
Unlikely scenarios (but not literally impossible)
Using Boltzmann's model of statistical entropy, the plate could spontaneously heat on the far side.
It is a miracle...or magic
I'm sure there are more scenarios that could easily be imagined for each of the above categories.
