A320 FLT CREW DEPARTING DEN AT MAX GROSS WEIGHT RECEIVES ECAM 'ENG 2 EGT OVER LIMIT' AT THE SAME TIME A HEADING AND TURN DIRECTION ARE GIVEN BY ATC. THE FLT CREW TURNS THE WRONG WAY AND ARE ADMONISHED BY ATC.

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TKOF IN DEN AT MAX GROSS WT FOR THE CONDITIONS; REQUIRING TOGA; FLAPS 1+F AND APU BLEED ON. WE WERE ONLY LEGAL FOR RWY 25 WHICH GOES AGAINST DEN TWR PROCS FOR OUR PLAIN4 DEP. WHEN CLRED FOR TKOF; THE TWR CTLR TOLD US TO FLY A NON-STANDARD 245 DEG HDG AND THAT SHE NEEDED AN EXPEDITED CLB THROUGH 8000 FT FOR ARR TFC. WE ADVISED HER THAT WE WERE AT MAX GROSS WT AND THAT WE WOULD GIVE HER THE BEST CLB THAT WE COULD. JUST AFTER TKOF SHE RPTED RADAR CONTACT AND TOLD US TO TURN TO A HDG OF 130 DEGS. LITERALLY SIMULTANEOUSLY WITH HER 130 DEG TURN RADIO CALL WE HAD AN ACFT ECAM WARNING -- 'ENG 2 EGT OVER LIMIT.' THAT ECAM HAS THE POTENTIAL FOR AN ENG SHUTDOWN. NEEDLESS TO SAY; WE WERE DISTR. THE FO (PF) STARTED A TURN IN THE SHORTER DIRECTION (L) TO 130 DEGS AS WE WERE PULLING THE THRUST LEVERS BACK TO CLB PWR. THE #2 EGT IMMEDIATELY CAME BACK WITHIN NORMAL PARAMETERS AND WE DETERMINED THAT THE ENG DID NOT NEED TO BE SHUT DOWN. THE TWR CTLR CAME BACK ON AND SAID 'I GAVE YOU A R TURN TO 130 DEGS!' WE APOLOGIZED AND CONFIRMED THAT SHE STILL WANTED A R TURN TO 130 DEGS. SHE DID. DEP CTL TOLD US TO CALL THE TWR AFTER LNDG. THERE WAS NO ATC EVENT THAT WE'RE AWARE OF. USUALLY; WHEN A CTLR GIVES INSTRUCTIONS THAT DIFFER FROM WHAT THE CREW WOULD NORMALLY EXPECT TO DO; THE CTLR EMPHASIZES THE DIFFERENCE. (EXAMPLE -- 'ACR XXX TURN R; R TURN; TO HDG 130 DEGS.') SHE DID NOT DO THAT AND IT MIGHT HAVE HELPED IN THIS SITUATION. WITH OUR DISTR; WE MISSED THE DIRECTION OF TURN.