ALTDEV ALT UNDERSHOT ALT XING RESTRICTION NOT MET IN AN OPPOSITE DIRECTION TFC SITUATION.

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CLBING THROUGH FL260; ZJX ASKED IF WE COULD CROSS 20 DME S OF CRAIG VOR AT FL330. WE WERE CURRENTLY AT 48 DME S WITH A RATE OF CLB OF 2000 FPM PLUS. OUR WT WAS 154000 POUNDS AND OUR GND SPD WAS 360 KTS. OUR IAS WAS 300 KTS. COMPUTING THIS INFO; THE FO AND I CONCURRED THAT WE SHOULD BE ABLE TO REACH FL330 WITHIN THE 28 MI TO GO. AS A BACKUP; I COULD TRADEOFF SOME AIRSPD FOR AN INCREASED RATE OF CLB. THE FO REPLIED TO CTR; 'I THINK WE CAN.' CTR THEN CLRED US TO CROSS THE 20 DME S OF CRAIG AT FL330. I MAINTAINED A 2000 FPM RATE OF CLB UNTIL OUT OF FL300 AT WHICH TIME I NOTICED THAT THE OUTSIDE AIR TEMP WAS INCREASING AND OUR RATE OF CLB STARTED TO DECREASE. I THEN BEGAN TRADING AIRSPD FOR AN INCREASED RATE OF CLB. I ALSO INCREASED THRUST TO 'MAX ALLOWABLE FOR A 2 MIN PERIOD' (ACFT ENG LIMITATION). HOWEVER; THE OUTSIDE AIR TEMP KEPT INCREASING AND WE WERE ONLY ABLE TO MAINTAIN A 1000 FPM RATE OF CLB OUT OF FL320 AT 23.5 DME. APCHING 20 DME; WE WERE LEAVING FL32.5 AND WERE LEVELING OFF AT APPROX 19 DME. DURING THE LAST 1000 FT; THE ACFT STARTED DRIFTING TO THE L OF CTRLINE. I ELECTED TO MAKE NO TURN TO CORRECT IN ORDER TO ACHIEVE MAX CLB PERFORMANCE; AND THAT WE WERE STILL IN PROTECTED AIRSPACE. (INSIDE THE 4 MI EACH SIDE OF CTRLINE AIRSPACE). ABOUT 10 SECONDS AFTER LEVEL AT FL330 (AND REGAINING AIRSPD); CTR POINTED OUT TFC AT 11 O'CLOCK AND 8 MI AT FL310. OUR TCASII SHOWED NO TFC NOR GAVE ANY AURAL ALERTS. WE SIGHTED THE TFC (AT FL310) AND IT APPEARED TO BE MORE THAN 5 MI (OPPOSITE DIRECTION). 2 SECTORS LATER; AND PRIOR TO BEING TURNED OVER TO ZDC; ZJX ASKED US TO CALL QUALITY ASSURANCE AT ZJX OVER A POSSIBLE INCIDENT S OF CRAIG. OUR FLT PLAN SHOWED A NORMAL TEMP LAPSE RATE AT OUR ALTS AND POS. HAD THE INVERSION NOT BEEN THIS EXTENSIVE; WE WOULD HAVE BEEN LEVEL AT 330 PRIOR TO THE 20 DME. IN ACCEPTING THIS XING RESTRICTION; I WAS ASSUMING NORMAL FLT CONDITIONS. I WILL NO LONGER ACCEPT A CLRNC THAT REQUIRES OPTIMUM OPERATING PARAMETERS SUCH AS A CLB RESTRICTION. I DO BELIEVE THAT CTR SHOULD ASSIGN EVASIVE HDGS WHEN A POSSIBILITY OF A CONFLICT ALERT EXISTS (NONE WAS ASSIGNED); OR IMMEDIATELY ASSIGNED A LOWER ALT (IF STILL BELOW THE XING TFC ALT). COM WERE ALSO SOMEWHAT AT FAULT. 'I THINK WE CAN' WAS NOT A DEFINITE YES AND ALSO THE XING TFC'S POS WAS NOT STATED UNTIL WE WERE LEVEL AT FL330. THERE IS OBVIOUSLY A LOT LEFT TO BE LEARNED IN AVIATION SAFETY. YOUR DATA BANKS ARE A BIG STEP IN THIS DIRECTION. SUPPLEMENTAL INFO FROM ACN 210906: AT FL325; ATC REPLIED 'SAY YOUR DME.' I RESPONDED 'JUST ABOUT 20 S;' AS THE DME COUNTER WAS READING 21 DME. ATC THEN REPLIED 'SAY YOUR ALT.' I RESPONDED 'FL325.' ATC THEN REQUESTED WE CALL THEM REACHING FL330. AT FL327 I REPLIED 'LEVELING AT FL330.