Could be a few things. First, you may be right that it's the fuel. I was having the same problem (bad warm starts) with my 955 recently. I put in a new tank of fuel and it began starting right back up again. Look around for a gas station that sells gas that doesn't give you problems and them keep filler your S3 there.
The second thing is that it might be your battery. When my last battery started to die (at about 6,000 miles) it was very hard starting, even warm. Try buying a
Battery Tender, or something equivalent, to keep your battery strong. If you battery is already dying, you may want to get another one.
Neither of these things require you to take it to the Triumph dealer, so try them first.
By the way, bad gas and weak batteries also afflict Japanese bikes. Don't go to the dark side.
Capt.