It's not a temperature sensitive spring, it's the wax/metal shaving paste that responds to temerature. This 'goo' is inside the little piston that actuates the 'valve' by expanding with an increase in temperature.
Have you checked the radiator cap?
Did you do the cooling system pressure test with the engine at operating temps?
Did you perform the combustion gas test under a simulated load with the engine at operating temps as well?
Was this motor recently rebuilt (indicating heads might need retorqued)? This one would be a likely culprit due to the fact that you said "It appears to be when I step on it".
Has this car been severely overheated just prior to this problem?