"It is warm today, and it is cool tomorrow."
You don't need て with the comma. http://ww8.tiki.ne.jp/~tmath/language/adjectives.htm#04
I had that problem too. Turns out the problem was that I was adding the word でも into the space of the comma. When I removed it, duolingo accepted it. However, I think that maybe it still should be accepted, as でも can mean "also" as well as "but", both of which seem applicable. Can I get someone to confirm/deny this?
@Guillermo2436 if you are still lost over there, it might be helpful to relate the usage of this ～く to what you see when you negate i-adjectives. You are basically using a clause to modify the next one「『今日は暖かく』→『明日は涼しいです』】this allows you to create a continuous sentence, similar to how you would connect 暖かく→ない in order to negate the concept of being described as 暖かい。