From a NY Times article:
Mr. Doohan requested that his remains be shot into space, and his family has arranged through Space Services Inc., a Houston company that provides "memorial spaceflights" and which also sent the remains of Mr. Rodenberry and Timothy Leary into space in a 1997 flight.
It'd be great if they could put him on the next shuttle, especially since the 1st shuttle in the fleet was named Enterprise after Star Trek fans wrote to the White House...
NASA article about the Enterprise