Do needs an object.
In "Is it supposed to do that?" that is the object. In your example, it's actually a demonstrative pronoun for "the act of getting hot."
In "Is it supposed to do like that?" like that can't be an object; the like is forcing a comparison between something and that. The "something" is the act of getting hot; and again that is a demonstrative pronoun, this time for "the act of getting hot in the way in which it does".
So you need a noun to be the object of do. It could simply be the word something.
Is it supposed to do something like that?
If you want to use an intransitive verb so you don't need an object, you could use behave (in your example):
Is it supposed to behave like that?
All of that said, the most idiomatic sentence is definitely the shortest:
Is it supposed to do that?