ACR FLC CROSSES AN ACTIVE RWY WITHOUT PERMISSION. FLC WAS DISTR BY ROUTINE TASKS. FLC PROMISE TO KEEP THEIR ATTENTION ON THE PRIMARY DUTIES AT HAND.

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IT WAS OUR FIRST FLT OF THE DAY ON DAY 4. DURING PUSHBACK WE STARTED THE L ENG FOR THE SINGLE ENG TAXI. THE ENG STARTED BUT THE TEMP PEAKED VERY NEAR THE MAX. IMMEDIATELY AFTER ENG START; THE FO CALLED FOR TAXI. THE TAXI INSTRUCTIONS WERE TO 'TAXI TO RWY 9L; HOLD SHORT OF RWY 13.' AFTER READING BACK THE CLRNC; INCLUDING THE HOLD SHORT INSTRUCTIONS; THE FO QUESTIONED THE DEP RWY SINCE RWY 27R WAS INDICATED FOR DEP ON THE ATIS. THIS RESULTED IN A CONVERSATION WITH GND CTL INDICATING THAT THE ARPT HAD BEEN TURNED AROUND AND RELAYING THE NEW WINDS. AS WE TURNED OUT OF THE RAMP AREA; PASSING AROUND THE FIREHOUSE; WE WERE ABLE TO SEE THE DEP END OF RWY 9L. IT APPEARED THAT WE WOULD BE #1 FOR TKOF. THE FO SENSING A NEED TO GET THE SECOND ENG STARTED IN TIME FOR A PROPER WARM UP BEFORE DEP; BEGAN TURNING THE R ENG. HE SIMULTANEOUSLY BEGAN READING THE TAXI CHKLIST. I ASKED HIM TO DELAY THE CHKLIST UNTIL AFTER ENG START SO HE COULD DEVOTE HIS ATTENTION TO THE ENG. I WAS ALSO CONCERNED ABOUT THE START EGT ON THE L ENG AND WAS WATCHING THE R ENG START. I DIVERTED MY ATTENTION FROM THE TXWY AND OUR TAXI INSTRUCTIONS. AS WE WERE APCHING THE INTXN OF THE TXWY AND RWY 13; I LOOKED UP AND SAW THE RWY MARKER. I THEN LOOKED TO THE APCH END AND SAW THE LNDG LIGHTS OF AN ACFT ON FINAL. SEEING THE ACFT I REMEMBERED MY 'HOLD SHORT' CLRNC. AT THIS POINT; WITH THE R ENG JUST STARTED (BOTH ENGS RUNNING) AND CLOSE TO THE RWY; I MADE THE DECISION THAT IT WOULD NOT BE POSSIBLE TO STOP WITHOUT ENCROACHING ON THE RWY. I ADDED PWR ON THE L ENG ONLY (THE R ENG HAD JUST SPOOLED UP TO IDLE PWR) AND CONTINUED ACROSS THE RWY. THE LIGHT TWIN DID NOT TOUCH DOWN UNTIL WE WERE WELL CLR OF THE RWY; ALTHOUGH; I'M SURE HE WAS NOT COMFORTABLE WITH OUR XING AND POSSIBLE JET BLAST. AT THIS TIME THE GND CTLR NOTICED OUR POSITION AND REMINDED US THAT OUR CLRNC WAS TO HOLD SHORT OF RWY 13. THE COPLT ISSUED OUR APOLOGIES AND WE CONTINUED; HEALTHY; THOUGH SOMEWHAT SHAKEN BECAUSE OF THE SERIOUS ERROR I HAD JUST MADE. OUR LATER DISCUSSION OF THE SIT BROUGHT TO LIGHT OUR SEVERAL ERRORS AND THE NEED TO KEEP OUR ATTENTION FOCUSED ON THE PRIMARY DUTIES AT HAND. THE FO WAS PLANNING ON A STRAIGHT; SHORT TAXI; EXPECTING RWY 27 BECAUSE OF THE ATIS. HE REACTED MORE TO THE CHANGE THAN TO THE 'HOLD SHORT' PART OF THE CLRNC. THAT PART DID NOT IMPACT ME EITHER SINCE I WAS STILL CONCERNED OVER THE HIGH START EGT OF THE L ENG. AS WE TAXIED AND HE BEGAN THE START OF THE R ENG; I WAS CONCERNED THAT HE WAS DOING TOO MUCH WHEN HE ALSO BEGAN THE TAXI CHKLIST. WHEN I ASKED HIM TO DELAY THE CHKLIST AND TRIED TO EXPLAIN WHY; THIS DIVERTED MY THOUGHT PROCESS FURTHER FROM THE JOB AT HAND OF SAFELY TAXIING AND COMPLYING WITH THE CLRNCS.