By Dubawi and out of Dar Re Mi, the youngster streaked to a seven-length success first time out.
He holds an entry in the Champagne Stakes next month but Gosden is keen to keep it low-key, for his next run at least.
Too Darn Hot is as low as 12-1 for next year’s 2000 Guineas already.
Gosden said: “He is a nice horse, but it is early days. He will go to a novice like Beatboxer did after his first start.
“We are not going to launch straight into Group company yet, as he doesn’t know enough about the world.
“We will win a novice first, then look at bigger targets.”