Unless the reflectivity of the oxide is extremely high, ellipsometry would be a suitable, non-destructive tool. Please note that model building is crucial in this method.
When it comes to destructive methods, there are depth profiling options in SIMS or XPS, or ultimately cleavage and just looking from the side with SEM would be options.
When you say "during high temperature exposure", does that mean during high T growth or just during an annealing process?
you can use techniques like ellipsometry, profilometry, or X-ray photoelectron spectroscopy (XPS). These methods provide valuable insights into the oxide layer's thickness and properties.
Santosh Kumar In the semiconductor industry the step height would be directly measured with a stylus profiler. These work from a few nm to (hundreds of) microns. I used one in the 1980's for ITO on glass and photoresist thickness etc. One example is: https://www.kla.com/products/instruments/stylus-profilers/alphastep-d-500
Search Google with the term "semiconductor profiler stepper".
RBS, Rutherford Backscattering Spectrometry works well for atomic composition as a function of depth for thicknesses in the 1 - 1000 nm range (thickness upper and lower limits depend on your accelerator energy and film atomic mass). Method is nondestructive but needs to fit into accelerator chamber.
XRD, x-ray diffraction can also be used to measure thin film thicknesses. It works well for about 100 nm to 10 micron thicknesses. It is sensitive to phase content.