A HDG TRACK POS DEV OCCURS WHEN THE FLC OF A DASSAULT FA10 IS DISTR WITH A COOLING PROB AND A FULL LOAD OF IRATE PAX ON THE SID DEP PROC OUT OF FLL; FL.

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WE WERE CLBING ON RADAR VECTORS TO INTERCEPT THE THNDR TRANSITION ON THE FLL 9 SID. THE FO WAS VERY INEXPERIENCED AND I ONLY HAVE ABOUT 15 HRS IN TYPE. WE WERE FULL OF PAX ON A HOT DAY FOR A LONG FLT; SO THE PAX WERE EDGY. CLBING THROUGH ABOUT 9000 FT; THE PAX WERE COMPLAINING LOUDLY ABOUT THE CABIN TEMP. WE TRIED USING OUR NORMAL SYS KNOWLEDGE AND THE CHKLIST TO COOL OFF THE CABIN. THE FO WAS NOT MUCH HELP WITH THE CHKLIST OR COMS WITH ATC; SO I SOON BECAME LOADED UP. WE WERE UNABLE TO COOL OFF THE CABIN; SO THE PAX DEMANDED A RETURN TO OUR ARPT OF DEP. WE ADVISED ATC WE NEEDED TO RETURN; AT APPROX 14000 FT; WHEN THE CTLR MENTIONED THAT WE 'MIGHT' BE FLYING ON THE WRONG OUTBOUND RADIAL AND HE WAS GIVING US A COURSE CORRECTION. EVERYTHING LOOKED OK TO ME; BUT WE STARTED VECTORS FOR OUR RETURN BEFORE I COULD DOUBLECHK. PUSHY; ANGRY PAX VOICING PROBS TO AN INEXPERIENCED FLC DURING A CRITICAL PHASE OF FLT CAUSED THIS SIT. WE SHOULD HAVE SLOWED DOWN. I SHOULD HAVE TOLD THE PAX TO WAIT A MOMENT WHILE I REQUESTED A VECTOR AND LEVELOFF FROM ATC. IF WE WERE FLYING STRAIGHT AND LEVEL; I COULD HAVE TOLD THE FO TO FLY WHILE I WORKED THE CHKLIST AND WORKED WITH ATC AND THE PAX.