Not all manufacturers adhere to the same limits, but almost all commercial grade parts that I've seen go from 0 C to 70 C, and that's almost always an ambient air temperature. Industrial grade normally goes -40 C to around 100 C. Military grade and automotive parts are similar, going from around -55 C to 125 C and up. The actual component maximum temperature limits are higher. The maximum ambient temperature is based on the junction-to-ambient resistance (when there's a junction, or case-to-ambient resistance), maximum junction (or case) temperature, and the maximum power.
I asked about the 60 C recommendation because I haven't seen any parts rated to 60 C.