The internet is surprisingly devoid of an accurate explanation of this, so let me try to break it down. First you need to know that "sou desu ne" (そうですね）is WEIRD to hear...it should be "sou desu nee" (そうですねえ）basically always.
You'll notice when I write Japanese in Romanji I put spaces in, which is important because the words don't always delineate themselves without writing actual Japanese (Katakana + Hiragana + Kanji). "Desu" and "nee" are both sentence particles, which is a concept that English simply doesn't have. "Sou" means something to the effect of "this (conceptual) thing here," "kou" is "this (conceptual) thing near me," and "ano" is "that (conceptual) thing over there." That pattern happens a few times, for example with "koko" ("here"), "kono" ("this physical thing here [description of object]"), and "kore" ("this physical thing here" [no description required, inferred from context]).
I know that's a lot of information just to define "sou," but it's important to understand that while it translates to "this," it specifically means "this conceptual thing we're both aware of right now." So what does that refer to? It's just whatever you said right before that. Let's try introducing one word to start making meaningful sentences. "atsui" (あつい）means "hot", but when spoken it's important that the intonation of the "tsu" be high, otherwise you've just said "thick." Now I can start to construct actual sentences talking about the weather (of course).
There are three conversational patterns to walk through in order to answer your question: "desu nee", "desu ne?", and "desu ka?" Those question marks I added on purpose to identify the two phrases that are questions, but of course Japanese doesn't have that punctuation.
"atsui desu nee" (あついですねえ) means "it's hot [expecting agreement]" and is basically always followed up by the other person in the conversation saying "sou desu nee!" which just means "it sure is!" It's very important to note that the particle "nee" (ねえ) does not make the sentence a question, so the appropriate response is just to agree. "desu" doesn't have any particular translation to English, it's just the Distal style (polite) particle that connects the words on either side.
"atsui desu ne?" (あついですね) means "it's hot-right?" The particle "ne" makes the sentence a question where the speaker is seeking confirmation. Disagreeing would get awfully complicated, but the answer should just be "hai. atsui desu yo" (はい。あついですよ）, which means "yes. it's hot!" "Hai" is the Distal form of "yes," and "yo" is another particle with no translation, but it makes the statement a little more emphatic (hence the exclamation mark). To your point about the effect of how this is said, it's not the accent that you need to get right per se, it's the pronunciation. The "ne" at the end should be said with a rising intonation, very similar to English actually. Think of how we say "right." vs. "right?", it's exactly the same. The rising intonation at the end of the sentence makes it a question. Also notice that there's only one "e" here unlike the two before. Japanese doesn't have syllables, it has "moura" （もうら）which is a unit of sound, and every moura gets the same amount of time when spoken. So the "nee" before is two moura, "ne (ね)" then "e (え)," which you'll often see written online as nē. This particle "ne" is only one moura, which changes the meaning and pronunciation.
"atsui desu ka?" (あついですか）means "is it hot?" Ending with the particle "ka" makes the sentence a question without the presumption of agreement. A typical response would simply be "hai. atsui desu" （はい。あついです） which of course means "yes. it's hot." I left off the "yo" to drop the emphasis on the sentence because the question was not presuming agreement like before.
That's an awfully long answer to a short question, but you did ask for an accurate translation :) Hope this helps.