Pathogen destruction is a function of time and temperature. Generally speaking, a compost bin at 140F/60C for an hour will kill most pathogens, or 130F/55C for a day, or 120F/49C for a week. And generally, compost bins will hold a peak temperature for between 24-72 hours before slowly dropping again, while adding fresh material will make the temperature rise again. Part of the reason time matters is because it isn't just heat that kills pathogens - it's also compost microorganisms that physically kill pathogens in the bin.

Getting compost very hot like 160F/71C like you say will kill pathogens quickly but it's not only unnecessary, it's also harmful, as a lower temperature will result in a more diverse culture of bacteria in the finished compost. Personally I aim for about 140F/60C.

And anyway, note that I said above 120F. It sounded like the GP was having issues with their compost that made me think that 120F would be a reasonable target to shoot for given their current situation.