Save stop time to a helper. Helper state persists through automation restarts, ha restarts, and OS restarts.

Check the helper every minute. Or, just run until the stop time is reached, and create an automation to check and restart the timer when HA restarts.

i would probably do it with two+ automations. Something like:

ON automation:

• trigger:
  • time pattern - beginning of every 3 hours
• then:
  • start timer with duration 37 minutes (select your timer helper)
  • Turn on AC unit

OFF automation:

• trigger:
  • Manual Event
    • event type: timer.finished (case sensitive!)
    • event data : entity_id: timer.[timer_helper_entity]
• then:
  • turn off AC unit

STARTUP_CHECK automation:

• trigger:
  • when home assistant is started
• if:
  • state - timer helper is idle
  • AC is on
• then:
  • turn AC off

Note 1: make sure the timer helper has restore state and time when HA starts enabled

note 2: automations using the timer.finished event will not trigger on startup if the timer expires when Home Assistant is not running.

note 2a: the third automation is for your edge case that you reboot/shutdown HA when the OFF automation was supposed to fire. it should ensure the AC turns off after the timer was supposed to be finished and HA is started. this automation does not account for if the AC is turned on manually and you restart HA.

i can get you the .YAML or pictures when I'm at a computer.

Make sure you have this option checked: