Thermostat for heating and cooling
Simply set your thermostat to &quot;fossil&quot; or &quot;gas/oil&quot; mode
Most thermostats out there support what you describe, as it turns out, as gas furnaces control their blower automatically by default, and only use the G terminal as an override to turn the blower on when the system is otherwise not running.  So, simply set your thermostat of choice to &quot;fossil&quot; or &quot;gas/oil&quot;, and you'll be set.
(If you're having trouble finding the option, check the installer's manual for your thermostat.  Older electronic 'stats had a small switch inside that set this, while newer ones have a software option instead.)