when I want to measure the activity of an enzyme in different temperatures and the buffer that I use is Potassium Tris Acetate, should I adjust pH of buffer in each different temperature?
Excellent question. The pH of a buffer solution does change with temperature, so to keep the pH constant throughout the experiment, the pH of the buffer should be adjusted to be the same at each temperature. An alternative strategy would be to use a buffer whose pH doesn't change significantly over the temperature range. Tris has a fairly large pH shift with temperature. If the pH you are using is not too high for it, HEPES would be a better choice, and MOPS would be even better.
https://www.promega.com/-/media/files/resources/technical-references/temperature-dependence-of-ph-for-common-buffers.pdf
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