1To warm or heat something up — food, a drink, one's body, a room, etc. A very common everyday verb. 温める is typically used for food and the body, while 暖める is preferred for warming air or a room.
冷めたご飯を電子レンジで温める。
I heat up cold rice in the microwave.
寒い日には、しょうが湯を飲んで体を温めるといい。
On cold days, it's good to drink ginger tea to warm up your body.
帰ってくる前に部屋を暖めておいたよ。
I warmed up the room before you came home.
お弁当、温めますか？
Would you like your bento heated up?
彼の優しい言葉が私の心を温めた。
His kind words warmed my heart.
2To hold on to an idea or plan rather than acting on it right away — to let it develop and wait for the right moment. A figurative use, as in 構想を温める ('nurture a concept') or 企画を温める ('sit on a plan').
このアイデアは何年も温めてきたものだ。
This is an idea I've been sitting on for years.
彼は長年温めてきた小説をついに出版した。
He finally published a novel he had been nurturing for years.
企画を温めておいて、タイミングを見て発表しよう。
Let's sit on the proposal and announce it when the timing is right.
3To rekindle an old friendship or renew ties with someone after time apart. Almost always seen in the set phrase 旧交を温める.
同窓会で昔の友人と旧交を温めた。
I rekindled old friendships at the class reunion.
帰省の際に、久しぶりに幼なじみと旧交を温めることができた。
On my trip home, I was able to reconnect with a childhood friend after a long time.
4To keep something advantageous to oneself rather than sharing it — a relatively rare usage, limited in modern Japanese to specific contexts.
彼は有利な情報を自分だけで温めていたらしい。
It seems he was keeping the advantageous information to himself.