B737-700 FLT CREW NEGLECTS TO TURN THE WINDOW HEAT ON. THE ACFT BECOMES COLD SOAKED AT FL410. FLT CREW TURNS ON WINDOW HEAT UPON ENTERING ICING DURING DSCNT. UPON ARR IT IS NOTICED THAT THE EYEBALL WINDOWS HAD SHATTERED.

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DUE TO A TSTM APCHING BWI; TOLD WE COULD NOT HOLD AT THE GATE. WE TAXIED TO DEICING PAD TO WAIT WHILE THE FIELD WAS CLOSED. CAPT ASKED ME TO SEND DISPATCH A MESSAGE INFORMING THEM OF THIS. EXPECTED DELAY WAS TO BE AROUND 40 MINS. WHILE I WAS TYPING THE DISPATCH MESSAGE; THE CAPT SHUT DOWN BOTH ENGS WITHOUT CALLING FOR THE SHUTDOWN CHKLIST. UPON NOTICING THE ENGS SHUTTING DOWN; I DID MY AFTER LNG AND SHUTDOWN FLOW; TURNING OFF THE WINDOW HEAT DURING THIS PROCESS. WHEN WE STARTED UP AND DEPARTED; WE USED THE APPROPRIATE CHKLIST BUT NEVER TURNED THE WINDOW HEAT BACK ON. DURING DEP; WE WENT THROUGH LIGHT; MAYBE OCCASIONAL MODERATE RAIN; BUT GOT SPD BELOW 250 KTS BELOW 10000 FT. WE CLBED TO FL410. DURING CRUISE; WE HEARD 3 LOUD BANGS/POPS THAT SOUNDED LIKE SOMETHING HVY DROPPED IN THE COCKPIT OR MAYBE A FLT ATTENDANT SLAMMING THEIR BINS. THE CAPT SAID IT WAS PROBABLY ACFT POPPING(?) UPON DSCNT INTO LOS ANGELES; THE WINDOWS STARTED TO FREEZE UP AND THE CAPT NOTICED THE WINDOW HEAT WAS OFF; SO HE TURNED IT ON AND WE OPENED UP OUR WINDOW VENTS WHILE INCREASING THE COCKPIT AIR TEMP. DURING DSCNT WE WENT THROUGH 1 CLOUD WITH LIGHT TURB BUT NO RAIN. WE LANDED UNEVENTFULLY. UPON LEAVING THE ACFT; I NOTICED THAT BOTH WINDOWS OVER EACH PLT'S HEAD WERE SHATTERED. WE FEEL THAT THE POPPING NOISE DURING CRUISE WAS WHEN THE WINDOWS BROKE BUT CAN'T BE SURE. IN FACT; WE CAN'T SAY FOR SURE THAT THE WINDOWS WERE NOT BROKEN WHEN WE GOT THE ACFT. WE FLEW 2 LEGS PRIOR TO THIS BUT THESE WINDOWS ARE COVERED BY GREEN SUN FILTERS AND I THINK THE ONLY REASON I NOTICED THE WINDOWS IN LOS ANGELES WAS THAT THE OVERHEAD GATE LIGHTS WERE SHINING THROUGH THESE AND I HAD RECENTLY FLOWN ANOTHER ACFT WITH THESE WINDOWS BROKEN ON MEL. MAINT THINKS THEY BROKE WHEN WE TURNED THE HEAT ON AND SUGGESTED THAT IF A SIMILAR SITUATION ARISES; DON'T TURN HEAT ON WITH AN ALREADY COLD WINDOW. THE MEL FOR INOP WINDOW HEAT SAYS ONLY TO KEEP SPD BELOW 10000 FT; WHICH WE DID. THE WINDOWS SHOULD NOT HAVE BROKEN BY THE WAY WE FLEW THE PLANE AND WE ARE WONDERING IF WE SHOULD HAVE TURNED THE HEAT ON OR NOT ONCE AIRBORNE FOR A LONG TIME. ALSO; OUR PROCS FOR SHUTTING DOWN AN ENG SAY NOT TO MOVE ANY SWITCHES EXCEPT THOSE CALLED BY THE SHUTDOWN CHKLIST. DOES THIS MEAN THAT WE KEEP THE START SWITCHES IN L CONTINUOUS FOR THE ENTIRE TIME WE ARE SHUT DOWN; OR IS AN AFTER SHUTDOWN FLOW EXPECTED?