B777-200 FLT CREW HAS HDG DEV DURING GAR AT SFO.

Narrative

AS WE WERE ON FINAL; THE TWR INSTRUCTED TFC TO CROSS RWY 28L FROM R TO L. IT APPEARED AS IF THE TFC MIGHT NOT CLR IN TIME. FROM MY PERSPECTIVE LOOKING STRAIGHT DOWN THE RWY AND SEEING THE TAIL OF THE ACFT; IT DID CLR THE RWY; HOWEVER WHEN WE WERE AT APPROX 100-200 FT; THE TWR ORDERED US TO GO AROUND. WITH NO TIME TO QUESTION THE CALL; WE EXECUTED A GAR AND WERE BUSY WITH THE MANY RELATED DUTIES. WE HAD; AS I RECALL; REACHED 3000 FT. AS I WAS BUSY WITH THE AFTER TKOF CHKLIST AND SEVERAL OTHER DUTIES; THE TWR CTLR GAVE US A HDG CHANGE. THE CAPT HAD BEEN HAND FLYING THE APCH. I REACHED UP AUTOMATICALLY TO DIAL IN THE NEW HDG ON THE MCP BUT SIMULTANEOUSLY REMEMBERED AND SAW THAT THE AUTOPLT WAS ENGAGED AND SAW THE CAPT'S HAND ON THE HDG SELECT KNOB. AS SEVERAL OTHER THINGS IN THE HVY WORKLOAD ENVIRONMENT WERE PRESSING; I TURNED MY ATTN TO THEM; LEAVING THE HDG CHANGE TO THE PF. A VERY SHORT TIME LATER ATC ASKED TO VERIFY THAT WE WERE ON THE NEW HDG. WHEN I LOOKED UP; WE WERE JUST TURNING TO THE NEW HDG.