Nickel polymer electrolytes have long been known to have unexpected properties. Careful studies of (i) conductivity as a function of temperature for PEO8:NiBr2 over the range 25 less than or equal to T less than or equal to 180 degrees C; (ii) conductivity at 150 degrees C of PEOn:NiBr2 over the composition range 8 less than or equal to n less than or equal to 200; and (iii) complementary differential scanning calorimetry and Variable-temperature polarizing microscopy (VTPM) measurements, are reported. In conjunction with extended x-ray absorption fine structure results reported earlier, these measurements suggest that the complicated dependence of conductivity as a function of temperature can be explained in terms of phase separation of the salt in the amorphous region followed by melting of salt-rich spherulites as the sample is heated from 140 to 180 degrees C, without the need to invoke explanations based on the degree of hydration. It is also suggested that phase-separated NiBr2 particles are present at room temperature in all samples that have been preheated to 140 degrees C in order to dry them and also in anhydrous concentrated films. It is possible to make dry films of PEO15:NiBr2 but not of PEO8:NiBr2. Attempts to reproduce the remarkable enhancement of conductivity of rehydrated films of PEO8:NiBr2 observed by other workers were consistently unsuccessful.