AFTER AN UNEXPECTED TEMP INCREASE; A C650 CREW EXPERIENCED PERFORMANCE DIFFICULTIES DUT TO THE ACFT GROSS WT AND CONDITIONS.

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EVENT/SIT: APPROX 1 HR INTO THE FLT; CRUISING AT FL430; ZAB INSTRUCTED US TO DSND TO A LOWER ALT FOR TFC. WE REQUESTED A HIGHER ALT DUE TO WX AND FUEL PLANNING CONCERNS. WE WERE THEN INSTRUCTED TO CLB TO FL450. APPROX 5 MINS AFTER LEVELING OFF AT FL450; WE ENCOUNTERED PROGRESSIVELY UNEXPECTED HIGHER OUTSIDE AIR TEMPS. CONCERNED WITH THE ACFT'S DECREASED PERFORMANCE; WE REQUESTED A LOWER ALT WITH ZAB. ZAB ADVISED US THEY WOULD HAVE A LOWER ALT IN 5 MINS. AFTER THE SECOND REQUEST FOR A LOWER ALT WE REQUESTED A VECTOR TO GET A LOWER ALT SOONER. AT THAT POINT THE ACFT PERFORMANCE WAS DETERIORATING RAPIDLY DUE TO HIGHER OUTSIDE AIR TEMP AND WAS SLOWLY UNABLE TO MAINTAIN ALT. ZAB ADVISED US THAT WE HAD LOWER TFC AT FL430 IN OUR 1 O'CLOCK POS. WE WERE GIVEN A LOWER ALT WITH A 20 DEG L HEADING VECTOR. WE WERE AWARE OF THE LOWER TFC INDICATED ON OUR TCASII AND CTR'S ADVISORY. AT NO POINT DID WE HAVE A TFC ALERT OR RA ON OUR TCASII. MY FO AND I CALLED ZAB SHORTLY AFTER LNDG AND DISCUSSED THE SIT. ZAB INFORMED US THAT THEY ARE REQUIRED TO HAVE A 5 MI SEPARATION BTWN ACFT AND THAT WE WERE WITHIN APPROX 4.5 MI FROM THE OTHER ACFT. I BELIEVE A COMBINATION OF EVENTS LED UP TO THIS SIT. ENCOUNTERING UNEXPECTED AND PROGRESSIVELY HIGHER AMBIENT AIR TEMPS AT CRUISE ALT CAUSED A SLOW DEGRADING EFFECT OF ACFT PERFORMANCE.