Relative Humidity plays a big part in being able to have sweat evaporate off your body, so a dry 120F wouldn't be too bad I guess. Sweating in 102F with about 70% humidity was about as much as I could handle, but I was also in it for about 8-9 hours. Hydration is key.
Here, have some charts and graphs (in F):
https://www.weather.gov/arx/heat_index