Do you want this for all or for a specific protein? In the living cell, a prepared cytosol or after purification?
One simple way would be to plate the cells after thermal stress and measure how many survived. This would measure the denaturation of the most temperature sensitive protein the cells require for survival.
To measure survival of a specific protein, measure its biological function (e.g., enzymatic activity). The advantage of this is that it can be done in a crude cytosol, w/o purification. Just spin down aggregated material.
For measurements on purified proteins, fluorescence is probably easiest. This can be an environmentally sensitive Trp-residue in the protein, or a dye that changes fluorescence after binding to the hydrophobic core of a protein (e.g., 8-Anilino-1-naphthalene sulphonic acid (ANS)).
Just one word of caution about kits: If you have understood a method and were able to implement it, you can always think about whether a kit would simplify your life enough to justify the higher cost. But to use a kit without such understanding will likely put you into a soup.
There is a method for measuring thermal denaturation of proteins in cells, called CETSA. The idea is that thermally denatured protein will precipitate. The cells are exposed to various temperatures, lysed, and centrifuged. The amount of the specific protein of interest is then measured in the supernatant. The more denaturation that occurs, the less of the protein remains in the supernatant. This method can also be done with cell extracts instead of live cells.
No kits. The problem with preciptiation is that it is concentration-dependent. Denaturation occurs in stages, some reversible and some irreversible. If you have relatively pure proteins, then you might try circular dichroism, but you need an expensive instrument for that and it doesn't work well for protein mixtures since the transitions are mixed. If you are lucky you can run a native gel of culture supernatant (or capillary zone electrophoretic separation). The denatured protein might shift in mobility or shape enough that you can see it. The gel method can also size sieve, so it good for protein mixtures. You can also typically confirm the identity of the protein and denatured protein bands with a Western blot. Unfortunately, gels aren't particularly quantitative, which is where CZE comes in. I would run the native gel first with Western to see if you can get a separation on heat-treated samples at various times and temperatures, confirm ID by Western blot, then migrate to CZE if necessary to get quantitation. Note, for CZE of proteins you need good capillary coatings. You can look up some of my papers on dynamic coatings for protein separations by CE (EOTrol and UltraTrol) to see how.