While flying across the U.S. before the Atlantic attempt Stewart lands and exits the plane. While doing a quick inspection of the airframe he approaches the engine and puts his hand on one of the radial engines cylinders which would have still been several hundred degrees, so should have resulted in a serious burn.
The real Charles Lindbergh was never allowed on the set of the film. Jimmy Stewart said if he showed up, all the cast would walk off. Lindbergh was hated for his pre-WW2 actives with Nazi Germany.