If your K type thermocouple is welded correctly to the metal part, you will have a good measuring instrument.
If your K type thermocouple is welded correctly to the metal part, so the joint between the thermocouple and the metal part must be either a weld connection or a fastened connection with a threaded insert, if you do that, you will have a good measuring instrument. You can use thermocouples within the magnetic field to read the temperature correctly. The measuring instrument must have sufficient isolation so if it isolates the magnetic field frequency, there will be no interference in the thermocouple readout. The important thing is that the thermocouple must be attached correctly to the metal part as well.