Do you have to use the adverb "gorąco" for describing weather? Is using the adjective form "gorący" also grammatically correct?
Depends on the exact sentence. Here, the subject is 'it'. I don't even know if it should be called a dummy pronoun here, because it doesn't get translated into Polish at all - the Polish sentence is subjectless. So such a subjectless sentence about 'it' will use an adverb in Polish.
However, you can still use an adjective to describe some noun, for example "This is a very hot day" = "To bardzo gorący dzień".