If one has an engine fire on takeoff without any thrust loss, why on earth would one want to increase thrust or need to do so? That makes no sense.
As one wouldn't
immediately reduce power on the smoking engine either despite the fire bell. It is giving some thrust output, use it in the initial climb. Once you are a bit a away from the tree tops and with the gear and flaps up, then you can shut down the engine completely.
Or so I was taught...
Escape Path