When potassium permanganate (KMnO\(_4\)) is heated at 513K, it undergoes a thermal decomposition reaction. The heat causes KMnO\(_4\) to break down, producing manganese dioxide (MnO\(_2\)), potassium hydroxide (KOH), and oxygen gas (O\(_2\)).
The decomposition reaction is as follows:
\[
2KMnO_4 \xrightarrow{513K} 2MnO_2 + K_2O_2 + O_2
\]
Thus, heating KMnO\(_4\) at 513K produces MnO\(_2\) (manganese dioxide).