AN ACR B737 FLC GET A 'WING BODY OVERHEAT' WARNING ILLUMINATED AND AFTER COMPLETING THE PROC DECIDE TO CONTINUE THEIR FLT'S FINAL DEST; OVERFLYING AN INTERMEDIATE STOP BECAUSE OF WX. THE RPTR REASONS NOW THAT RETURNING TO KTN MAY HAVE BEEN MORE PRUDENT. NO EMER DECLARATION.

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WE DID A NO BLEEDS TKOF FROM KTN BECAUSE OF A TAILWIND USING THE APU TO PRESSURIZE THE ACFT. AFTER RE- ESTABLISHING THE BLEEDS TO A NORMAL CONFIGN; WE GOT A MASTER CAUTION LIGHT AIR CONDITIONING 'WING BODY OVERHEAT R SIDE.' WE DID THE CHKLIST; TO SHUT OFF ALL BLEED AIR SOURCES TO THAT SIDE. THE LIGHT REMAINED ON; BUT IT TAKES TIME TO COOL AND THE LIGHT FLICKERED A FEW TIMES. WE CONTINUED CLBING OUT OF THE WX (LIGHT ICING TO ON TOP). CONTACTED MAINT CTL AND DISPATCH. WE CHANGED OUR ALTERNATE TO JUNEAU (A MAINT STATION AND THE WX WAS VFR AS COMPARED TO SITKA; OUR ORIGINAL DEST; WHICH WAS IFR AND I SUSPECTED LIGHT ICING). AS WE LEVELED OFF AT CRUISE; FL260; THE WING BODY OVERHEAT WENT OUT AND REMAINED OUT. WE LANDED WITHOUT ANY PROBS. THE MECH DID A PRELIMINARY INSPECTION AND FOUND NO BLEED LEAK. WE CHANGED ACFT AND CONTINUED ON. OUR DECISION TO GO ON TO JUNEAU AND NOT RETURN TO KTN OR LAND AT OUR DEST; SITKA; WERE BASED ON SEVERAL FACTORS. 1) AFTER ISOLATING THE R SIDE FROM ANY BLEED AIR; I KNEW IT WOULD TAKE TIME TO COOL AND THE CHKLIST DOES NOT CALL FOR AN IMMEDIATE LNDG. 2) THE WX AT SITKA WAS MARGINAL AND THERE IS LIMITED MAINT THERE; AND THERE WAS THE POSSIBLE CHANCE OF ICING ON THE APCH. THE WX AT OUR DEP ALSO HAD A CHANCE OF ICING. 3) JUNEAU WAS VFR. IT WAS OUR NEXT STOP AFTER SITKA. IT WAS A LARGER MAINT BASE THAN KTN. THE WING BODY OVERHEAT LIGHT WAS ON FOR APPROX 12-15 MINS BEFORE GOING OUT FOR GOOD. IF I HAD TO DO IT OVER AGAIN; I MIGHT HAVE JUST MADE A 180 DEG TURN AND LANDED BACK AT KTN. I WOULD LOOK AT CHANGING OUR CHKLIST COVERING THE WING BODY OVERHEAT TO READ 'IF LIGHT REMAINS ILLUMINATED AFTER A CERTAIN TIME; LAND AT THE NEAREST SUITABLE ARPT. CAUTION NO WING ANTI-ICE AVAILABLE ON THE EFFECTED SIDE.'