It’s worth changing both the cut out and the cooling fan stat provided the tangential fan is not worn,blades are likely to be full of grease if it’s a few years old and that could be a factor too (not pushing enough air round) in the cutting out etc.
Easy enough to repair.
i have replaced tonnes of these cutouts if it is the 4 wire (2 blue,2 white) at the top slide oven half way out take front section of lid off and change cut out 10 min job.never changed a fan on these always the cut out.