Driving without serpentine belt - overheating?

I would suspect that two miles is the upper limit. I lost a belt on my Riviera 3800 due to the water pump bearing (bearing wears, pulley goes out of alignment, and belt won’t stay on). It was -10 out at least on the freeway. I drove probably a mile from one exit to the next and my temp guage was at the upper limit. I had just driven 40 miles so it was fully warmed up but it was ten below out too. I think if the car was fully cold, you could do two miles but it doesn’t take long to over heat.