B737-300 FLT CREW LEAVES #1 ENG RUNNING AFTER PARKING AT GATE IN MCI FOR ACFT COOLING.

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DISPATCHED WITH APU INOP; LATE DEP DUE TO UNRELATED MAINT ISSUE. AIR TEMP AT DEP 97 DEGS; HAD TO USE FLAPS 1 DEG IMPROVED; UNPRESSURIZED TKOF PROC; ACFT NEVER COOLED SUFFICIENTLY FOR PAX COMFORT ENRTE; AIR TEMP MCI WAS 96 DEGS. ON ARR AT GATE CAPT ELECTED TO LEAVE ENG #1 RUNNING TO KEEP PAX AS COOL AS POSSIBLE DURING DEPLANING; AFTER GND PERSONNEL PLUGGED IN ELECTRIC PWR AND THEN WALKED OFF WITH NO APPARENT INTENTION TO CONNECT GND AIR AFTER ENG SHUTDOWN. MCI OPS CALLED AND ASKED IF THERE WAS A PROB SINCE WE HAD NOT SHUT DOWN ENG #1. CAPT STATED THAT WE WANTED TO KEEP COOLING AIR FLOWING FOR PAX COMFORT. MCI OPS STATES THAT THEY COULD NOT HOOK UP GND AIR WITH ENG RUNNING. CAPT REPLIED THAT WE UNDERSTOOD THAT. APPARENTLY GND PERSONNEL ASSUMED THAT WE WANTED THEM TO HOOK UP GND AIR WITH ENG RUNNING WITHOUT ACTUALLY TALKING WITH US. NO ONE IN THE COCKPIT MADE ANY SUCH REQUEST; WE ALL UNDERSTAND THE DANGERS OF MOVING AROUND A RUNNING JET ENG AND WOULD NEVER ASK A FELLOW EMPLOYEE TO ENDANGER THEMSELVES IN SUCH A WAY.