B737 FLT CREW PROCEEDING DIRECT GLEAM FOR ILS RWY 31C AT MDW IS TOLD TO CIRCLE TO LAND RWY 22L; 31C GS NOW OTS. FO DESCENDS BELOW 4000 FT PRIOR TO GLEAM AS CAPT PROGRAMS FMC.

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RETURNING FROM A DIVERT DUE TO EARLIER FOG AT MDW; WAS CLRED FOR A VISUAL APCH AND TOLD TO CROSS GLEAM AT 4000 FT. FO WAS FLYING; AND JUST PRIOR TO THE EVENT; THE WINDS HAD CHANGED AND A NEW ATIS WAS PUT OUT. THE CTLR ADVISED US AND TWO ACFT AHEAD OF US TO DO THE ILS RWY 31C CIRCLE TO RWY 22L. ALSO; WITHIN A COUPLE OF MINUTES OF THIS; THE CTLR ALSO ADVISED THAT MAINT HAD TAKEN THE GS OTS SO HE ACTUALLY CLRED US FOR THE ILS RWY 31C GLIDESLOPE OUT CIRCLE TO RWY 22L. WE HAD PLANNED ON THE STRAIGHT IN FOR RWY 31C AND SINCE THE LNDG DISTANCE WAS NOT 'MAX BRAKING' THE FO WAS SET TO LAND. HAVING RUN BOTH RWYS; I PULLED THE OPC TO CHECK TO SEE IF HE COULD NOW CONTINUE TO LAND ON RWY 22L. DURING ALL THESE CHANGES; WHEN I LOOKED UP THE FO HAD DSNDED OUT OF 4000 FT PRIOR TO GLEAM; ACTUALLY CROSSING GLEAM AT AROUND 3200 FT. WE WERE VISUAL AND THE CTLR DID NOT SAY ANYTHING SO WE CONTINUED THE APCH AND LANDED ON RWY 22L. THE WORKLOAD ALWAYS CAN INCREASE RAPIDLY DURING CHANGING WX CONDITIONS; AND IN THIS CASE; A LOT OF CHANGES WERE GIVEN DURING A BUSY TIME IN THE APCH. PROBABLY THE SAFEST CROSSCHECK DURING THIS TYPE OF ACTIVITY WOULD BE NOT TO PRESET THE ALTITUDE WINDOW UNTIL PASSING THE INTERSECTION TO ENSURE AN ALTITUDE CHANGE WASN'T MADE EARLY WITH THE DISTRACTIONS AT HAND.