Is it possible to apply a Kalman filter to a 2D thermal problem?

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I have a transient thermal problem: I've created a 2D geometry with two different materials, I've put in an internal source, I've mashed it and solved the PDE. After a t time I can see how the structure diffuses the heat. I've taken different temperature points and I've put in a random noise to create something similar to a real case. Now I would like to apply a Kalman filter to get an estimate of my system but I think it's not the right filter to apply to a thermal problem. The equation of my problem it's the heat equation.