A B737 PIC ABORTS HIS TKOF ROLL PRIOR TO 40 KTS WHEN HEARING ANOTHER ACFT BEING CLRED ACROSS HIS TKOF RWY 34R AT SLC; UT.

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AT THE DEP END OF RWY 34R AT SLC; TWR ADVISED RWY 34R; CLRED FOR TKOF. WE COMPLETED THE BELOW THE LINE CHKLIST AND BEGAN TO SET TKOF THRUST. AT APPROX 40% N WE HEARD THE TWR CLR AN ACFT TO CROSS RWY 34R. I REMEMBER THINKING THIS WAS STRANGE BECAUSE WE WERE JUST BEGINNING OUR TKOF ROLL ON THAT RWY. I DID NOT ADVANCE THE PWR LEVERS BECAUSE OF A POTENTIAL COLLISION HAZARD. I COULD NOT IMMEDIATELY VERIFY THE RWY WOULD BE CLR OF THIS POTENTIAL TFC. ACFT WERE LNDG AND DEPARTING RWY 34L; RWY 34R; AND RWY 35. APPROX 1 SECOND LATER; I RETARDED THE PWR LEVERS TO IDLE AND REQUESTED THE FO ADVISE THE TWR WE WERE ABORTING THE TKOF. THE TWR ASKED WHY AND WE TOLD HER WE WERE CONCERNED ABOUT THE XING CLRNC OF THE OTHER ACFT. THE ACFT ATTAINED A SPD OF APPROX 40 KTS. NO REVERSE OR BRAKES WERE USED BECAUSE OF THE SLOW ACFT SPD. WE ROLLED TO THE BEST OF MY RECOLLECTION TO TXWY H3 AND EXITED THE RWY. I ADVISED THE PAX AND THE FLT ATTENDANTS WHAT HAD HAPPENED AND THAT WE WOULD TAXI BACK FOR TKOF. NO BRAKE COOLING PROCS WERE REQUIRED. THE TWR ADVISED US THE OTHER ACFT WAS AT TXWY H2. I DON'T REMEMBER HEARING THIS DURING THE XMISSION. ALL I HEARD WAS CROSS RWY 34R. I THINK ABORTING THE TKOF IN THIS SIT WAS THE BEST COURSE OF ACTION. WE PROCEEDED TO RWY 34R AND DEPARTED. I DON'T KNOW WHAT CAN BE DONE TO PREVENT THIS PROB FROM RECURRING EXCEPT NOT TO CLR AN ACFT TO CROSS A RWY THAT IS BEING USED BY ANOTHER ACFT FOR TKOF.