Learn Turkish: Biz o evde kömür sobası ile ısınmıyorduk. - We were not warming up with a coal stove in that house.

It comes from the verb ısınmak (to get warm). First, we take the root ısın-. Then we add the negative suffix. Normally this is -ma, but the -yor suffix always narrows the vowel before it, changing it to -mı. Next is the continuous marker -yor, followed by the past tense -du, and finally the personal ending for we, which is -k. So we get: ısın + mı + yor + du + k.

Why is it sobası instead of just soba (stove)?

Kömür sobası is a noun compound. In Turkish, when two nouns are put together to make a single concept (like 'coal stove' or 'apple juice'), the second noun gets a possessive ending. Since soba ends in a vowel, it takes -sı, making it kömür sobası.

Could I attach the word ile (with) directly to the word before it?

Yes, you will very often see ile attached as a suffix. Because sobası ends in a vowel, you add a buffer -y- and then -la (due to vowel harmony). So you could write this as kömür sobasıyla. Both versions are correct and mean exactly the same thing.

Why use ısınmak here instead of (to heat)?