Is there any reason that "Yesterday, it was a very hot day" would be incorrect?
Usual excuse probably. If this is the standard of English then I don't have any confidence in the standard of Spanish we are being taught.
Seems to me that it's more natural to say "Ayer fue caliente". Of course, we already that yesterday was day, we said is much in the word "yesterday".
Calor is a noun which really means 'heat'. El fuego produce calor = Fire produces heat.
Calurosa is the feminine form of the adjective 'caluroso' meaning 'warm' or 'hot' and as I understand it is not actually used that much except in describing weather. Es un día caluroso = it is a hot day. Like Duo's given sentence.
Caliente is an adjective meaning 'hot' as in hot to the touch. El horno está caliente = the oven is hot. Though I have seen it used for 'spicy' as well. La pimienta está caliente = the pepper is hot.
Edit One caveat here: You could use 'calor' for weather as well however you would use it with the verb hacer. Hace calor afuera = it is hot outside.
No, 'yesterday' in English can be a noun, so you could say "Yesterday was very hot", in Spanish ayer is an adverb, it cannot work as a subject, but you could say "Ayer hizo calor".