This article seems to conflate "spice ingredients" with spicy ingredients. I would have a hard time considering how food from cuisines that use (e.g.) aniseed, caraway, cardamom or poppy seed could be considered "spicy food".
Mean annual temperature also seems like the wrong thing to consider. The temperature ranges seem more important.
What is it like in other languages?
Spiced / Spicy (pungent)
Spanish: Especiado / Picante
French: Épicé / Piquant
Swedish: Kryddad / Pikant
English is just not very good at describing flavor. Looking at British food, there might never have been the necessity.
In German there's scharf (spicy) and pikant (slightly spicy). As well as würzig (spiced).