Brian's answer's great, but I'd like to add something.
Linux users generally aren't used to paying for software, and they tend to be more tech-savvy and possibly even "religious" on open-source issues.
For that reason, I'd really recommend keeping it simple - it's really just a small barrier to make buying the software at least as easy as stealing it.
I'd suggest that it nags or disables certain features (eg saving) after the trial period rather than dying completely. Just an observation, but feature-based restrictions seem more common in the linux world.
As an aside, making the linux version a "first class" version - decent installer etc will help.
If you're relatively small, or your program's relatively niche, there's a pretty small chance anyone will bother to crack it - so just concentrate on making a good product with a straight forward niggle once the time's up.