POTENTIAL CLOSE PROX BETWEEN TWO SMALL GA ACFT.

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ACFT X TOOK OFF FOR FLT TO W. PLT OF X THEN CALLED TWR SEVERAL MINUTES LATER FOR ARR INSTRUCTIONS. I THOUGHT THE PLT MIGHT BE EXPERIENCING SOME DIFFICULTIES DUE TO THE SHORT FLT. I ASKED THE PLT IF SHE WAS EXPERIENCING ANY DIFFICULTIES. HER REPLY WAS NEGATIVE AND WAS GIVEN STANDARD ARR INFORMATION. WHEN SHE REPORTED A COUPLE MILES OUT SHE WAS SEQUENCED TO FOLLOW SMA Y ON BASE WHICH SHE ACKNOWLEDGED. ACFT Y WAS CLRED FOR A TOUCH AND GO WHILE THE SPACING BETWEEN X AND Y DECREASED. AS Y WAS TOUCHING DOWN I DETERMINED THAT REQUIRED SPACING WOULD NOT EXIST AND ISSUED A go around TO X WHILE ON 1/2 MILE FINAL. HER REPLY WAS A go around WAS IMPOSSIBLE. I THEN ASKED ACFT Y TO INITIATE A TURN AS SOON AS POSSIBLE AFTER DEPARTURE TO ENSURE REQUIRED SEPARATION. TALKING TO THE PLT OF ACFT X LATER SHE SAID HER DOOR OPENED ON DEP. I THEN ASKED WHY SHE COULDN'T GO AROUND SHE SAID IT WAS TOO COLD INSIDE THE ACFT (OAT 5 DEG F). FORTUNATELY THE PLT OF ACFT Y WAS KNOWLEDGEABLE AND HAD THE BIG FLIC OF WHAT WAS GOING ON. AND ONLY BECAUSE OF THIS PLT A SYSTEM ERROR WAS AVERTED. MY THANKS TO HIM. IF ONLY ACFT X PLT WOULD OF CONFESSED HER SITUATION I WOULD HAVE GIVEN HER SPECIAL TREATMENT.