Jetstreams occur at height at the junction between hot and cold air masses. The temperature difference between the warm sector and the cold sector means the warm sector is a taller column of air and, consequently, the pressure in the warm sector at a particular height is greater than the pressure in a cold sector. This would initially lead to a flow of air at height from the warm sector to the cold but the coriolis effect rapidly takes over causing the air to flow parallel to the frontal surface. If there's a big temperature difference there's a big thermal wind, a jetstream.
The temperature change is an indication of passing through the front at altitude. Jetstreams tend to lie in the warm sector just below the tropopause so a sharp increase of temperature at jet cruising heights means you are near a jet.