It actually depends on what type of air mass the jet stream is picking up. It starts from a polar standpoint, as that air at the poles is colder, and therefore denser, than the warmer air contained at the equator. All wind is caused by moving air, generally speaking, from colder areas like the poles moving to and replacing warmer areas, like the equator. So generally speaking, yes, the air being brought in by the jet stream is cooler, representing a higher pressure air system that replaces the warmer air, which is a low pressure air system. Thunderstorms are the type of precipitation brought on by cold fronts, which is the primary type of front produced by the jet stream. Sometimes, though, the jetstream scoops down into the Gulf of Mexico and pulls up lots of warm moist air. It really depends on the type of air mass and the pressure the jet stream is interacting with as to what type of weather will be produced.