If I understand correctly, heading is usually measure relative to the pole (either magnetic or true). Traveling at a constant heading can't be approximated as travelling straight ahead when near the pole. The extreme case being heading to 180° and crossing the south pole.
Althought there are not many aircraft in this situation as explained in this question, using the heading may not be relevant. How is the navigation handled is such area? Is the heading used?
Near the poles 'polar grid navigation' is used. By placing a rectangular grid over the pole, aligned with the prime meridian, a local coordinate system is created. Aircraft fly constant grid courses near the poles.
For your example crossing the south pole approaching over the prime meridian the true course will change from 180° (T) to 000° (T), but the grid course will remain 180° (G) all the time.
Grid courses and true courses can be converted easily, this youtube video explains it nicely (although he gets the grid track in the wrong direction in the end, it should be 110°(G) instead of 290°(G))
