We prepared the sputtered Co/p-InP Schottky diodes which consisted of as-deposited, and diodes annealed from 200 °C to 700 °C. The annealed samples were cooled from the annealing temperature down to room temperature, and then, their current-voltage (I-V) characteristics were measured. Schottky barrier height (SBH) at 300 K slightly decreases from 0.80 eV (for as-deposited sample) down to 0.77 eV (for the sample annealed at 400 °C) with the annealing temperature and then again increases up to 0.91 eV for the sample annealed at 700 °C. The I-V measurements were made in the sample temperature range of 60–400 K. It is seen that the SBH for each diode monotonically increases with increasing the sample temperature up to 400 K. In the sample temperature range of 60–400 K, the Co/p-InP SBD annealed at 400 °C has a lower ideality factor value than those of the as-deposited and 200 °C annealed SBDs at each sample temperature. Thus, remarkable apparent improvement of the diode parameters has been achieved by means of the thermal annealing. The improvement in the Co/p-InP interface due to the thermal annealing process has continued without deteriorating at each measurement temperature from 60 K to 400 K. Therefore, it has been concluded that the thermal annealing process translates the MS Schottky contacts into thermally more stable Schottky contacts.