The problem is that Temple was a conservative Republican who, among other things, campaigned for Nixon. Both Reagan and Temple came from the pre-1960s Hollywood that was run by Republican moguls, before it got gutted by TV and trust busting and became fertile ground for counterculture. I doubt even with her stardom that she could beat Mondale in the primaries, or that she would take issue with Reagan enough to run in the first place.
I have wondered why Temple didn't serve in Reagan's administration, given that she served in Nixon's, Ford's, and the elder Bush's. She was a conservative Republican and it's hard to believe she would've backed Reagan's Democratic opponents, but I can't help but wonder if there was personal animosity there..