DSC Metal hysteresis (melt/cryst)
Disclaimer: the following is based on using DSC data for organic materials.
Is the melting temperature of Indium (156 C) just at the temperature where your sample exhibits a phase transition / decomposition?  In general, I suggest to use the flat indium pellets and to record their melting for calibration of the DSC, rather than their recrystallisation. This is likely described in the manual of your DSC.  (I does not hurt to have a look at DOI: 10.1007/s10973-015-5186-8, or similar, either.)
Because of its transient character, it is worth to keep an eye on the heating rate / cooling rate while recording DSC data.  Provided enough sample material, sometimes a quick screening with 10 K/min is followed by a second recording at a rate of 4  K/min (or slower).  While the endothermic peaks related to melting may be sharp, the ones for the recrystallisation are often shifted towards lower values because without proper seeds of crystallisation, supercooling may occur, especially organic samples and polymers.
I recommend to consider cyclic DSC, instead of a simple single-heating experiment, as this offers you additional insight about the sample in question. It is applied to characterize pure metals (like DOI: 10.1098/rspa.1996.0113), and may shed a light on the degree of crystallinity and processes of reorganisation of your polymer sample, too.  In the following, a DSC of polylactic acid:

(source)
Sometimes these differences about recording the melting point (pristine sample, after 1st / 2nd heating cycle) are spot on small molecule materials, too.  They may appear even if the sample did not incorporate solvent molecules.