You could use a template sensor (for each sensor you want to monitor):
trigger:
platform: template
value_template: "{{ (as_timestamp(strptime(states('sensor.date_time'),'%Y-%m-%d, %H:%M')) - as_timestamp(states.sensor.living_room_temperature_1.last_changed) ) > 600 }}"
Restating home assistant will update the last_changed attribute though. So if your sensor hasn’t changed for 500 seconds then you restart, it will take another 600 seconds of no updates after the restart for it to trigger.
If that’s important there are ways to rectify it: