Moving average solves the problem, but gives you a new one. How to calibrate, since fluctuations means that you are not picking up the correct temperature. Have you tried to establish how the fluctuations relates to the true temperature? Does it add a significant measurement offset?

Another thing: What response time do you need? That affects your ability to low-pass-filter.

Is it possible to use a pyro sensor instead? Remember that yur thermocouple may have a limited life span on that vibrating surface.