its not A/C blowing, its the furnace blowing cold air thru, have them check the pilot.
if the pilot is off, light it, if it keeps going out, replace thermal couple.
if pilot on, and have them turn thermalstat all the way up, it should call for cycle, if nothing happens, replace battery or thermalstat
when it call for cycle, furance should click, if not, may need to clean sensor or replace limit switch.
if it cycles, and run for a while and die, you may need replace control board, usually there is a LED, showing error code, check that.
