The core of the jet stream is found in the warm air, above
the level of the cold air tropopause but below the warm air tropopause. If the
temperature of the cold air tropopause is -40°C, the temperature in the warm
air at that level would be -34°C. Above the tropopause in the cold air the
temperature will be constant at -40°C but in the warm air the temperature will
continue to decrease with altitude, at about 2°C/1,000ft, up to the warm air
tropopause ten or twelve thousand feet higher. This means that the warm air
tropopause temperature would be about -54°C.
Therefore, if you cross the jet stream from the cold sector
to the warm sector below the core of the jet the temperature will increase
(from -40°C to -34°C) but if you cross the jet stream from the cold sector to
the warm sector above the core the temperature will decrease (from -40°C to
-54°C). The jet core (highest wind speed) is found at the level where
there is maximum pressure gradient and zero temperature gradient (-40°C to
-40°C). If you stand with your back to
the wind and have cold air on your left you are below the core of the jet and
wind speed will increase as you climb. If you stand with your back
to the wind and colder air is on your right you are above the core of the jet
and wind speed will decrease as you climb.