Thomson operate a single queue system at Gatwick. We like to get there about three hours beforehand (well, I do, my wife's not so keen when it's an early flight) and we've never had a problem. The queue can be long, but moves pretty quickly. Obviously you can't rely on this, though - at a Thomas Cook check-in the previous year the queue stretched so far we queued for an hour to check-in.
Your flight time complicates it though - will the check-ins open at 03:15?
I suggest that, nearer the date, you look at Gatwick Departures to see how early Thomson flights depart on that day of the week. I remember flying with EasyJet last spring - flight was about 07:15 and there were 15 EJ flights before us. ( We got there for 4:30 am, and were through check-in and security in under 20 minutes).
The good news is that you should fly through security at that time in the morning. The bad news is that there'll be very little open in the departures hall - but at least you'll get a seat easily - they seem to be removing seats all the time, to make way for more shops.