Many years ago, I needed to compensate a microwave device for thermal expansion. It was for aircraft use, and had to tolerate vibration but also had to be very light. There was a good range of bi-metal sheet material available then, and there must be more today with millions of mechanical thermostat blades punched out of it.
The configuration I ended up was a circular washer, which maximises the stiffness for a given amount of temperature deflection. If applied to a pendulum bob, it would be like this diagram. In order to “flatten” minor distortions in the bi-metal washer, it needs a sufficiently strong spring force to get contact all round the outer circumference. Provided nothing bottoms out, this does not affect the temperature sensitivity.
You do need to calculate the compensation needed from the expansion coefficients of the pendulum materials. If the worst comes to the worst, it is possible to stack several disks in series, though this spoils the simplicity of the design.
