Note that this can result in water/lava drips not being visible, and thus taking a lava bath.
Most of the following suggestions are configurable in the game's Options menu, accessible by pressing Esc. You can still see the FPS in other ways, such as downloading GUI mods. Note that the debug screen is known to cause more load to your system, resulting in lower FPS than you would normally achieve, so your FPS might increase as soon as you close the display. The frame rate will be shown under the Minecraft version at the top left.