would depend on the convection rate, wouldn't it?
If the microorganisms could reproduce and diffuse randomly and quickly enough (earth bacteria can do so in several hours under good conditions), maybe some would waft across to an upward convection movement before reaching heat-sterilizing depths.
If the rate and conditions don't work for Jupiter, maybe other gas giants or ice giants in our solar system or elsewhere would have the right conditions.
The problem I see is how life originates under those conditions, but maybe it could start on an earthlike or europa-like body and then get transferred on rock or ice meteorites.
I wouldn't rule out gas-giant life.