Translation:It is warm today.
温かい：For objects you can touch or feel, like "warm coffee", "warm shower", and can also used in abstract sense, like "a warm welcome"
暖かい：For surroundings. Like "warm room"
So actually 暖かい is more proper here. But this difference is sometimes ambiguous, and I think even Japanese sometimes mix them together, since I found many websites teaching how to tell these two kanji written in Japanese.
あたたかい can be also read as あったかい colloquially. You will often see あったかい and つめたい in vending machines for drinks in Japan.
Is there a difference between あつい and あたたかい？Or in other words between hot and warm? (Non native English speaker here)
In English, 'hot' is hotter than 'warm'. Like I'd use warm if it was 24C but hot if it was 38C.
今日は暖かいです was not accepted as correct. The problem seemingly being the use of kanji instead of hiragana.
The sentence "今日はあたたかいです" does not contain the word "weather". The word for weather is: 天気 (hiragana: てんき).
Is it technically correct here to translate this as "it's warm today"? Should that be kyo ga atatakai? Wa suggests emphasis on today. Should it be "today is warm" despite the Wnglish being uncommon?
The difference between wa en ga is about function and meaning. The distinction between topic is about communication, introduction and external relations and subject has an internal, grammatical function in the sentence syntax.