What is the thermal stability of potassium phosphate and why?


I assume you mean as a powder, not as an water solution. Potassium phosphate is deliquescent.
At elevated temperatures, phosphorus oxides are released as the compound decomposes.

How elevated? I want to prepare a sample of pure, dry potassium phosphate in my school's lab so I plan to crystallise it then place it in an oven. Will anything happen when I heat it over a bunsen flame during crystallisation?

If you want to prepare a pure sample of tribasic potassium phosphate, The Merck Index gives two references (both in German).
Janecke, Z. Physik. Chem. 2127,75 (1927) OR

Simon, Shultz, Z. Anorg. Allgem. Chem. 242, 331 (1939).

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