If I’m reading your need correctly, then maybe using a virtual switch as an 11 minute delay timer and trigger for the Automation might work.
Automation
If
Time Period with Time Day equal Sunrise plus 30 minutes to Sunset.
Temperature (whatever source) is equal or above 78
Outlet is Off
Virtual switch is Off
Then
Turn On Outlet and Auto Turn Off in one minute.
Turn On Virtual switch and Auto Turn Off in eleven minutes
As for the Temperature, the new Weather feature isn’t working for me. So if it’s not working for you either, then install the SmartWeather Station Tile from template in the IDE as it works flawlessly in my Automations set to my zip code. As for running local, the weather requirement needs access to the internet to get the weather conditions so it can’t run local unless you use a multisensor or motion sensor for the temperature condition.