Fastest temperature sensor for a bimetallic strip
To get fast temperature measurements, you need two things:


A fast temperature sensor
Fast electronics


It shouldn't be too hard to get fast electronics. ADCs tend to have the speed advertised fairly clearly, and unless you mis-configure some kind of internal digital filter will not normally delay the data by more than one sample or so, so I'll talk about fast sensors.  A fast sensor needs:


A low heat capacity
A low thermal resistance link to the sample


Low heat capacity tends to mean small. A thermocouple would usually be a good choice. Make sure it is a bare junction, it should just look like two thin wires welded together. When I wanted good, small thermocouples I used to make my own from suitable wire, as commercial ones can have big blobs of metal or plastic covers which slow down the response time.

Low thermal resistance to the sample means short distance, and that distance filled with something with a high thermal conductivity. Welding directly to the bimetal strip would be best, solder would be next, followed by high quality conductive epoxy (e.g. Epotek H20E, not the stuff used for PCB repair). A non-electrically-conductive epoxy is not as good, so if you can set up your ADC so that it does not need to be electrically isolated from the bimetal strip that will help.

With a thermocouple formed by welding &lt;100um diameter wire, welded onto a sample, I have been able to measure temperature changes into the low hundreds of Hz. There is a technique in Physics called "AC calorimetry" where this is commonplace, and you might find more useful information in papers on the subject.