There's another "lump" was observed after melt. Without information about the scale of y-axis, the initial Wt of your materials and sensitivity of your equipment, it is most likely both can be artifacts of the baseline from your equipment.

Worth noting, it is a good practice to define the thermal events by, e.g. Tm by peak position or onset of the starting/end points, or Tm can be not comparable.

Hi,

Is it possible that your samples may some residual solvent that would have a boiling point between 82 and 87 deg C?

As the the solvent evaporates small amounts of your sample may crystallise.

Please ramp down the temperature increase to 2deg/min and check if the exothermic peak intensifies. If it intensifies it must be due to recrystallization of any impurity present with the HDPE .This recrystallized material may melt after 160 or 200 deg C.So request is to extend the DSC upto 250 deg C and check if you observe any melting peak.