Yesterday topped 38 degrees Celsius/100 degrees Fahrenheit and today was forecast to be similar.* As I left this morning, I said to my wife ‘Stay cool’ (in the temperature sense). She said ‘What does that mean?”. I said ‘It means – stay – cool. Don’t get too hot.’
I don’t know about anyone else, but I would never tell anyone to stay cold. Correspondingly, in winter, we would tell people to stay warm, not stay hot.
*And it was. As I type this mid-evening, a cool change has blown in, but my house is still very hot. I’ve opened all the doors and windows, but it hasn’t had much effect yet.