What is the min. Temp. A landlord's supposed to set a thermostat at in the apt for a tenant? And does/can it vary at different times of day(in a 24hr)

If there is a minimum legal requirement for a thermostat in a rental property then it would be a municipal law. You can find out if your town has any such law by contacting the Health Dept. But you should be aware that not all towns have such a law. If there is no specific law then the general rule is a "reasonable" temperature.