If there is no temperature drop across the heater pipes then this would suggest that there is no air flowing over it.  
 
More modern heater units have an internal flap(s) that can totally shut off air supply, allow 100% of air to flow through/over the heater matrix or divert 100% of the air AWAY from and bypassing the heater matrix.  
 
So, you could be looking at some form of flap being jammed and stuck in the wrong position or similar flap control failure.