What is the surface temperature or a pulsar?

Let's look at less exotic stellar cinders first.

When they are first formed, white dwarfs probably have surface temperatures over 100,000 K, but they very quickly cool down to 50,000 K and below over the course of millions of years.

Neutron stars, which are what hosts the 'pulsar mechanism' are also formed very hot, in the cores of supernovae, and probably start out with temperatures of several billion degrees since the core of the star that collapsed to produce them was at least this hot. But at these enormous temperatures, matter radiates energy at a fantastic rate, and so without further internal sources of energy, the neutron star 'cinder' cools off in a matter of hours or days to temperatures that are probably well below a million degrees overall. But, because of the powerful 'trillion gauss' magnetic fields, particles can be accelerated near the surface of the neutron star to very high energies. The magnetic fields can also become tangled and 'reconnect' releasing stored up energy onto the surface. Finally, matter can rain down along the magnetic field lines and impact the surface releasing lots of energy into what may be local hot spots. All of these sources of energy can keep small regions of the surface heated to 100s of MILLIONS of degrees for limited periods of time...perhaps like the flares we see on the sun from time to time.