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Esfriar vs. ficar frio vs. arrefecer

While esfriar, ficar frio, and arrefecer can all mean to get cold regarding food and drinks, the choice depends heavily on regional differences (Brazil vs. Portugal) and the level of formality. In general, esfriar is the standard action verb in Brazil, ficar frio describes the resulting state, and arrefecer is the standard term in Portugal but signifies formality in Brazil.

Esfriar

A2
This is the most common active verb used in Brazilian Portuguese to describe the process of something losing heat. It refers to the action of cooling down. It is direct and used in almost all contexts in Brazil.
Beba o seu café antes que ele esfrie.
(Drink your coffee before it cools down.)
Eu vou esperar a sopa esfriar um pouco porque está muito quente.
(I will wait for the soup to cool down a bit because it is too hot.)
A comida vai esfriar se você demorar para vir para a mesa.
(The food will get cold if you take too long to come to the table.)
Deixe o bolo esfriar na bancada.
(Let the cake cool down on the counter.)

Ficar frio

A2
This phrase literally translates to to become cold or to stay cold. Unlike the verb esfriar which implies a process, ficar frio focuses on the change of state or the end result. It is very colloquial and frequently used in casual conversation.
Que pena, a pizza ficou fria enquanto assistíamos ao filme.
(What a shame, the pizza got cold while we were watching the movie.)
O chá fica frio muito rápido no inverno.
(Tea gets cold very fast in the winter.)
Não coma isso agora, espera ficar frio.
(Don't eat that now, wait for it to get cold.)
Se deixar a janela aberta, o jantar vai ficar frio.
(If you leave the window open, dinner will get cold.)

Arrefecer

B2
This verb acts as a synonym for esfriar. However, in Brazilian Portuguese, arrefecer sounds formal, literary, or technical (often used for engines or emotions). In European Portuguese (Portugal), arrefecer is the standard, everyday word for food cooling down.
É preciso deixar o guisado arrefecer antes de guardar no frigorífico.
(You need to let the stew cool down before putting it in the fridge.)
O pão acabou de sair do forno e está a arrefecer.
(The bread just came out of the oven and is cooling down.)
Cuidado para o café não arrefecer demasiado.
(Be careful so the coffee doesn't cool down too much.)
O leite ferveu e agora está a arrefecer.
(The milk boiled and is now cooling down.)

Summary

To sound natural in Brazil, use esfriar for the process of cooling and ficar frio when describing that the food has become cold. If you are in Portugal, arrefecer is the go-to word for everyday situations. In Brazil, using arrefecer for a cup of coffee will sound overly formal.