The terminology might make an exacting answer difficult. Herein, I'll make some simplifying assumptions in order to provide a clear answer.
The OP is positing that there exists a language-independent "canonical meaning" such as, "The heat in the room was intense because all the windows were shut." Given that, the questions are:
- How is one to say that?
- What is the difference in meaning between the given sentences?
- What are other ways to say that?
Each of the OP's example sentences have the same meaning, but has a different focus on perspective, emphasis, or importance. Let's look at a more simple example:
- John baked the cake, which smelled like vanilla.
- The cake, that smelled like vanilla, was baked by John.
- The cake, that was baked by John, smelled like vanilla.
- The cake, which had been baked by John, smelled like vanilla. (Note: "had been" is functioning similar to the word "being" in the OP's sentences. It's only a different perspective due to the tense/aspect of this example.)
- John had baked the cake, which smelled like vanilla. (Again: "had" is a different tense.)
All of these sentences have the exact same semantics if one thinks of semantics as "what really happened, objectively speaking". The difference is what the writer/speaker wants to present/designate as focus or importance in the sentence. That could depend on the intention of the sentence or some context such as the preceding sentence, the following sentence, or some other wider context. The choice in sentence phrasing is a matter of writing style and skill. (And that is outside the scope of this answer.)
Another variant is the use of a restrictive clause, which imparts additional information.
- The cake which had been baked by John smelled like vanilla.
- The cake that smelled like vanilla was baked by John.
The difference between restrictive and non-restrictive clauses have been discussed at length elsewhere. For the purpose of this answer, it's important to understand the following:
Both restrictive and non-restrictive clauses share a core set of semantics: there is a cake, it was baked by John, and it smelled like vanilla.
The use of the restrictive clause implies additional information: there exists a cake that smelled different (maybe chocolate!) or there's a cake that was baked by someone else.
The non-restrictive clause (parenthetical phrase) has the effect of decreasing the importance of it's semantic contribution to the sentence.
Finally, the OP uses the word "now". To me, this is also part of the perspective emphasis, independent of the "what actually happened" semantics. An observer, who is deictically in the time "now" is observing that the heat in the room is "now" intense because the windows had been shut in the past.
All of the OP's sentences have the same meaning; the difference is perspective, emphasis, and importance of the sentence elements. No one way is "right": it's the author's job to provide the desired perspective, emphasis or importance.