Blower fan comes on and shuts off about 30 seconds later, even though heat and air control is off on the wall thermostat.

Remove the stat and see if the problem persists. May need new batteries too.

I do not have a stat with battery. It is the old manual type for heat and air option switch with blower on/auto switch.

Ok, remove the stat from the sub-base anyway and tell me if it persists. Thank you