Both are adjectives but...
Caliente is not used for weather, it's used for substances such as food, water, surfaces etc. It comes from the verb 'calentar' = to heat up
Caluroso can be used for weather (in LA countries) and a warm welcome. In Spain however, caluroso is very rarely used at all and they prefer to use 'hace+noun' for weather: ie. Hace calor = It's hot
I was going to ask the same question myself. I have an additional query - I have a memory that when referring to oneself or another person the choice of word is vital as one has sexual connotations - but I cannot remember which. Any help?
Yes, caluroso is an adjective derived from the latin noun 'calor' (heat). The 'u' is a recent change and it can also be spelled correctly as 'caloroso', so neither is wrong.
Caluroso is derived from calura (seldom used), and caloroso (seldom used) is derived from calor.
'Calura' is actually the feminine form of the masculine noun 'calor' which is derived from the latin 'calor'. So I guess we could assume it has influenced the orthographic change in the Spanish 'caluroso'