FO OF A B737-500 STARTS TKOF ROLL BEFORE BEING CLRED FOR TKOF.

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TWR GAVE HOLD SHORT INSTRUCTIONS AND ADVISED AN 8 MIN DELAY FOR RELEASE FOR FLOW CTL INTO DEST ARPT. NEW CAPT AND JUMP SEAT OCCUPANT. (ANOTHER COMPANY CAPT ON SAME ACFT.) BEGAN CONVERSATION ON COLD WX OPS AND SUGGESTIONS FOR NEW CAPT ON ENG ICE USE FOR THIS PARTICULAR TKOF (BLOWING SNOW). TWR GAVE INSTRUCTIONS DURING THIS CONVERSATION AND I REPEATED THEM BACK -- AND I'M STILL NOT SURE WHAT THE TWR INSTRUCTIONS WERE OR WHAT I REPEATED BACK (IE; 'CLRED FOR TKOF;' OR 'POS AND HOLD'). ONCE ON THE RWY; THE CAPT EXCHANGED THE CTL OF THE ACFT FOR MY RADIOS. I REMARKED; 'MY ACFT; WITH BRAKES RELEASED' AND COMMENCED TKOF. AT 80 KTS OF AIRSPD (APPROX 1000 FT DOWN THE RWY); THE TWR CLRED US FOR TKOF AND TO FLY RWY HDG. WE CONTINUED AND WERE TOLD AT 1000 FT AGL TO CONTACT DEP. AFTER THE CLRNC FOR TKOF; WHILE WE WERE ON THE TKOF ROLL; THE REST OF THE TKOF WENT NORMAL. HOW PROB AROSE: 1) TALKING DURING HOLD SHORT PERIOD. 2) SELECTIVE HEARING OR POOR LISTENING SKILLS. 3) NO CLARIFICATION WITH ATC. 4) POOR CREW COM. 5) THE BIGGEST FACTOR WAS MY ASSUMPTION THAT SINCE THE CAPT DID NOT SET THE PARKING BRAKE BEFORE OR AFTER RELINQUISHING ACFT CTL TO ME; THAT WE WERE CLRED FOR TKOF. COMPANY POLICY IS TO SET PARKING BRAKE ANY TIME YOU COME TO A COMPLETE STOP. WITH NO BRAKE SET; I ASSUMED IT WAS A ROLLING START TKOF. SOLUTIONS: NO TALKING ON THE HOLD SHORT. CLARIFY POS AND HOLD OR CLRED FOR TKOF WITH THE CAPT AND ATC. BETTER COMS AND WORK ON LISTENING SKILLS. FINALLY; DO NOT ASSUME -- INQUIRE -- COMMUNICATE!