A B737-300 FLT CREW TOOK OFF WITH ENG ANTI-ICE ON WITH OAT 32 DEGS C.

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DURING INITIAL TAXI OUT; MY FO DID NOT GET A SATISFACTORY TEST ON THE ENG ANTI-ICE WITH IDLE THRUST AS IS A COMMON OCCURRENCE ON THE FLEET. HE DECIDED TO WAIT UNTIL I ADVANCED THE THROTTLES AND HAD MORE PNEUMATIC PRESSURE TO VERIFY THE VALVES WOULD OPEN; HOWEVER HE DID NOT MENTION THIS TO ME. AS WE TAXIED OUT; WE RAN THE CHKLIST AND I DID NOT CATCH THE FACT THAT THE ENG ANTI-ICE VALVES WERE STILL OPEN. I DON'T HAVE AN EXPLANATION AS TO WHY I MAY HAVE BEEN TEMPORARILY DISTR. ATC DID NOT INTERFERE WITH OUR CHKLIST AS WE WERE ABOUT THE ONLY AIRPLANE ON THE RAMP. PERHAPS I TURNED MY ATTN SOMEWHERE JUST AS HE CALLED FOR THE ANTI-ICE VALVES ON THE CHKLIST. I ALWAYS MAKE IT A HABIT TO TOUCH THE CTL THAT IS CALLED FOR ON THE CHKLIST; BUT AGAIN; I HAVE NO EXPLANATION FOR HOW I MISSED THE ANTI-ICE VALVES IN THE WRONG POS. AS A RESULT; WE TAXIED OUT AND TOOK OFF WITH THE ENG ANTI-ICE VALVES IN THE ON POS WITH AN OAT OF 32 DEGS C. SHORTLY AFTER LIFTOFF; WE GOT A 'THERMAL ANTI-ICE ON ABOVE 10 DEGS C' ON THE FMC SCRATCH PAD. AT THAT POINT; I REACHED UP AND TURNED THEM OFF.