I mean, you could just convert the Farenheit or Celsius degrees to radians like they were angle degrees. “Bake at 6.109 radians for 45 minutes” still can mean “Bake at 350 degrees for 45 minutes” if you accept the implicit Farenheit scale. Radians would still be ambiguous regarding the base scale used, but it’s as ambiguous as “degrees” is so not really an issue.
So I mean, there’s no real reason to do it but also no reason you can’t.