MR2 start up problems

After a long period of starting and running beautifully my MR2 Turbo suddenly developed starting problems. The engine starts without difficulty but stammers and back fires for 3 to 5 minutes gradually improving until it will run up to the rev limit without difficulty. The engine will start and run well for the rest of the day. I have just spent $600 to have the engine tuned but after a couple of weeks the problem reappeared. Any suggestions as to what is the cause of the problem.