Hello Addison, Yeh the difference is exactly what you mentioned: 熱い means hot .When referring to physical heat like hot water or hot weather it means that the thing referred to has higher than desirable temperature, giving off heat or causing a sensation of heat and burning. 暖かい means warm .When the climate ,the body or water is warm it means it has or produces a comfortable and agreeable degree of heat.

There are actually some more kanji used for those kinds of words. 暑い is more commonly used than 熱い when talking about (too) hot weather. 暖かい is also used when talking about the weather. They are used in the same way as the words for cold/cool: 暑い (too) hot <> 寒い (too) cold, talking about the weather 暖かい warm <> 寒い (too) cold, same as above 熱い hot <> 冷たい cool, talking about a sensation/generally 温かい warm <> 冷たい cool, same as above So... If you go out and it's 35 degrees hot (celcius) outside it's 暑い！ If you eat icecream in this heat it's 冷たい. Maybe you disregard the heat and go for a cup of 熱いコーヒー. If you go out and it's warm and nice it's 暖かい！ If you go out and there's a snowstorm outside it's 寒い！ When you return to your cozy home it's 温かい. You can see some example sentences if you look them up at http://www.alc.co.jp/ .