Wurtzite GaP nanowires are interesting for the direct bandgap engineering and can be used as templates for further growth of hexagonal Si shells. Most wurtzite GaP nanowires have previously been obtained with Au catalysts. Here, we show that long (similar to 500 nm) wurtzite sections are formed in the top parts of self-catalyzed GaP nanowires grown by molecular beam epitaxy on Si(111) substrates in the droplet consumption stage, which is achieved by abruptly increasing the atomic V/III flux ratio from 2 to 3. We investigate the temperature dependence of the length of wurtzite sections and show that the longest sections are obtained at 610 degrees C. A supporting model explains the observed trends using a phase diagram of GaP nanowires, where the wurtzite phase is formed within a certain range of the droplet contact angles. The optimal growth temperature for growing wurtzite nanowires corresponds to the largest diffusion length of Ga adatoms, which helps to maintain the required contact angle for the longest time.