That's true of French. In Spanish, however, you actually have 'heat' (calor), but yes, you use the verb 'to have', too ('hot' would be 'caluroso' or 'caliente' depending on the sentence). And I know we're translating "minulla on, etc." as to have, but (and now this is a question) it's more like a "hot is on me" kind of meaning in Finnish, isn't it?
Interestingly, according to Wiktionary, this has many of the same senses it does in English:
fervent, angry, stolen, conducting electricity, physically attractive, radioactive.
But not spicy, attracted, popular, close to guessing, or with cop presence (unless they just forgot to add those).
To say spicy in Finnish you could use "tulinen", fiery.
As for popular, there was a horrid phrase some time back - "kuuminta hottia", taking the English word hot and turning it into a Finnish word (hottia) with the Finnish for "hottest" before it. (A non-Finnish person once said that you can take any word and put an i in the end and it becomes Finnish: tractor - traktori, band - bändi, hit - hitti...)
For guessing we do use the hot and cold system, "kylmenee" - getting colder and "kuumenee" - getting hotter.
You can also say "kuumottaa", which is a feeling of either nervousness or excitement.
The Finnish verb "olla" contains two English verbs: to be and to have. This instance is about having - the sentence would literally translate as "do they have hot", not "are they hot". Having is always expressed with "onko" - "onko heillä leipää", "onko sinulla kahvia". Being is expressed with the other construct - "ovatko he suomalaisia", "oletko sinä iloinen".
As for why "hot" in Finnish is something to have instead of something to be - well, that's just the way it is :) They use the same structure in French, for example. It's a different way of understanding and observing reality, I guess.
Being French, I'm not sure I understand this sentence correctly. Is it like Ils ont chaud (these people suffer from heat) or ils sont chauds (these buns are hot, for example)? My guess would be the first due to structure to be + to whom + noun... The second option would be he ovat kuuma (if adjectives don't get plural, I'm not advanced enough)?
"Ovatko he kuumia?". It also has the potential alternative meaning of "are they hot (temperature-wise)?". I see you've studied German at least a bit, so perhaps it will help to know that the adessive case in "onko heillä kuuma?" has the same effect as the dative case in "ist ihnen heiß?". It is therefore about them feeling hot rather than being hot (to the touch), which English can be ambiguous about since both can be expressed with "are they hot?".
Yes, "he is hot" could mean "hänellä on kuuma", and it could also mean "hän on kuuma", which are not quite the same. The former is from an insider perspective (what he feels) and the latter is from an outsider perspective (what it would feel like if you were to touch him, or what he looks like if "kuuma" describes his appearance).