Worms are flesh and blood creatures, so they like the same temperature range that humans do, more or less. Your worms will thrive at around 75 degrees, but will have no problem surviving between 55 and 90 degrees (F).
The worm population will begin to die quickly above 95-100 degrees if they do not have a warmer area in their bin to escape to.
However, below 55 degrees, worms will likely not start dying until temperatures approach freezing. Studies also suggest that worm cocoons can stay viable in a frozen state for weeks or months until temperatures begin to rise again.