My 2004 Buick Lesabre cranks but will not turn over when the engine is warm, such as when I m stopping at a store for a half hour or so. When I wait for 1-2 hours it will start.

If the car is not cranking it could be one of several things. Starting with the easiest...... (1) bad battery (2) corroded battery terminals (3) bad connection at ground or starter (4) bad starter

Sorry I somehow hit post before finished.... I would check the battery terminals, but the problem is probably the starter, it is not uncommon for them to act up when the get hot...they get hot from the exhaust manifolds near them. Some cars have heat shields to keep the exhaust manifold heat off the starter.

Try your Ignition module. Once they go bad and get warm they will shut your car down as if you've disconnected the battery. After the car cools off, it will start right backup and run for a while until it gets warm again, and then it will shut the car down again. I've had this issue before and a new ignition module solved my problem.