Strange batch of potassium nitrate with lower than expected melting point
It might contain $\ce{NaNO3}$ as well as $\ce{KNO3}$. This paper by Foong et. al. cites some thermal measurements, such as melting point and heat capacity, that you could make with a thermometer and heater. Note that there are inflections in the heat capacity curve as the different components ($\ce{NaNO3}$, $\ce{KNO3}$ and the eutectic of the two) melt.

If you have access to a spectroscope, or even a hand-held diffraction grating, you could compare the spectrum with that from samples of known substances, such as $\ce{NaNO3}$, $\ce{KNO3}$, $\ce{NH4NO3}$ and $\ce{Ca(NO3)2}$.