There was a short lived series in the 80s about a family that is traveling together in the future dystopian society. I can only remember one scene and it has bugged me for years. The scene is one in which the teenage son joins the villain army as a ruse. When his loyalty is tested (by being asked to place his hand in a flame) he passed. The flame turned out to be cold.
You're remembering the episode "The Zone Troopers Build Men" from the 1985 show Otherworld, about a family lost on a parallel Earth that has a mix of different types of societies in different "zones", including some with futuristic technology. The scene in question can be seen starting at around 18:30 in the video below: