I'm a little new here, but I just wanted to add to Steve's post a ditto and say that you can find silicone caulking that is paintable, it just costs a couple more bucks/tube than does the regular acrylic.
I live up in ND and run a custom painting bus. I run into stress cracks and temperate cracks DAILY. Many of these are apparent problems during the winters, but during the summers they are gone or vice versa.
If it's up against door casing though, I'm guessing it might be some slight cosmetic damage that may have been caused during the actual erection of the door. If it's relatively small hole (1"-2" x 3/4"), I'd just put some lightweight spackling on a small drywall knife and drag it from the joint outward, let it dry, prime & paint.