1Pleasantly warm or mild, neither cold nor hot. 暖かい is used for air temperature and weather; 温かい for the warmth of things you touch (food, water, etc.).
今日は暖かいから、コートはいらないね。
It's warm today, so you won't need a coat.
春になって、ずいぶん暖かくなってきた。
Now that spring is here, it has gotten much warmer.
寒い日には温かいスープが体にしみる。
On a cold day, warm soup really hits the spot.
湯たんぽのおかげで布団の中が暖かい。
Thanks to the hot water bottle, it's warm inside the futon.
2Kind, considerate, and warm-hearted in personality or attitude. Written 温かい for this sense.
落ち込んでいたとき、友人が温かい言葉をかけてくれた。
When I was down, my friend offered me some kind words.
この町の人たちはよそ者にも温かい。
The people of this town are warm even to outsiders.
失敗しても、上司は温かい目で見守ってくれた。
Even when I failed, my boss watched over me with a kind eye.
温かい家庭で育ったことに感謝している。
I'm grateful to have grown up in a loving home.
3Warm and mellow in color, light, or tone — giving a soft, cozy impression (typically reds, oranges, yellows). Written 暖かい for this sense.
リビングは暖かい色の照明にすると落ち着く。
The living room feels calm with warm-colored lighting.
彼の絵は暖かい色使いで、見ていると心が和む。
His paintings use warm colors that soothe you as you look at them.
4Flush with money; financially comfortable. Colloquial, especially in the set phrase 懐が暖かい (one's wallet is full). Written 暖かい for this sense.
ボーナスが出たばかりで、今は懐が暖かい。
I just got my bonus, so my wallet is flush right now.
給料日前は懐が暖かくないので、外食は控えている。
Money's tight before payday, so I'm cutting back on eating out.