how many times; how often
Used to ask about the number of occurrences or repetitions. Can also be used adverbially without a particle.
I've watched this movie many times.
I called him many times, but he didn't answer.
how many degrees
Used to ask about temperature, angles, or other degree-based measurements.
What is the temperature today?
How many degrees is this angle?
How many times have you watched this movie now?
What is today's high temperature?
No matter how many times I explain it, he doesn't understand.