That's what I was taught as well. Heat can make things "feel better," but sometimes it's at a cost of greater pain.
With ice, as the body reacts to the cold, and then the removal of the ice, you get that tide flow of oxygen rich healing blood. As I've learned it, ice will not hurt you, but heat "may" exacerbate, making ice the "go to" when there's any doubt.
I've been a proponent of ice all the time, but Andy has encouraged me to give heat a try,...I'm a reluctant and stubborn soul, but I'm open....
I still love my ice packs, and will swap out, ending in ice (that's my compromise!)
Sic vis pacem para bellum.
Listen not to what they say about you. Listen to what they whisper.