Your iPad is designed to run at speeds that will make the iPad warm and maybe hot, by your definition. When the iPad approaches temperatures that could potentially cause damage, the processor and graphics chips are throttled or in other words, they lower the clock speed and processor slows down. This deliberate slowdown can result in dropped frame rate and this is normal.
Very few games have been optimized for the M4 chipset yet and thus will have sloppy code that results in excessive heat and slowdowns. As LotusPilot stated, cases decrease the thermal efficiency by insulting the back of the iPad, the major source of cooling for the iPad. High screen brightness also causes much higher battery consumption and a big increase in heat. As processors need to ramp up to handle higher temperatures, they require more energy and increase in battery consumption. The higher discharge rate of the battery contributes to the heat issue.
Until the game software is optimized by the game company you can reduce brightness, and reduce resolution, shading and other game options, you’ll need to manually perform these functions. However, once the game is updated, you should be able to resume game settings that result in more realistic play.