2007 subaru impreza station wagon

I am at a loss... My subaru for 8 months has not
given me any teouvle other than the whining noise
when accelerating.  My car outta the blue started
to overheat (winter just came upon us).  I have
changed the thermostat, water pump, and had
head gasket tested. All in great condition.  My
mechanic couldn't figure it out (with his time). We
drove it home started cold of course (less than 3
miles) with 3 blocks it was hot as hell boiling over.  
Now the plugs were checked n changed so were
wires because of the roughness of engine while
running.  We had absolutely no heat only cold air
blew out. If the heater core was out would that
cause this particular stupid car to run rough
(wanting to stall) overheat and block hot air from
entering the cabin?