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This could be a problem with the heater core clogging up.
Here are a few things to try, feel the heater hoses and feel if there is a difference in temperatures.
If one hose is hot and the other is cold, try removing the heater hoses and flushing out the heater core using either compressed air or a water hose and see if you can clean out any obstructions.
If the heat gets better but not perfect, you may need to replace the heater core.
If both the heater hoses are cold, I would suggest bypassing the heater core and install a clear hose between the heater hoses.
Watch the coolant as it flows through the system.
If there is little or no coolant flow, there could be an issue with a water pump. If there are air bubbles in the system the system might not of been bled properly although you did the right bleed procedure with raising the front of the vehicle.
Can you check this first? And does this make sense?
OK, so the possible next step is a heater core blockage? Where will I locate both heater hoses? Are they in the engine compartment on the firewall closer to the passenger side? The water pump was replaced with the timing belt not so long ago so I do not suspect this.
If I remove the heater hoses, will I need to bleed the coolant system again?
Yes, the heater hoses are going to the firewall passenger side. And yes, once you remove the heater hoses you will lose some coolant, so bleeding the system again should be done.
How much success have you seen in removing heater core blockage with a water hose / air blast? If heater core blockage is confirmed and I am unable to remove blockage, what then?
Then you will need to replace the heater core itself.
The heater core is pretty common to cause this problem.
Is this an end user friendly operation or a dealer recommended activity?
It's actually a pretty big job to replace the heater core, that is why I would recommend cleaning it out. Backflushing is pretty easy but in order to replace the heater core you have to evac the freon, remove some of the dash. It's a 5 hour job.
Given what we've discussed so far, do I understand you correctly in that the most likely possible fix to my problem is to either clear a blockage in or to replace my blocked heater core?