If you have already looked around here at the info you should know that the heater core becomes blocked and gives no heat on drivers side.
There is a plastic restrictor in the outlet lower side to slow coolant enough to extract heat. This also allows sediment, crud, etc to collect at the far end on the core. since the ports are facing the passenger side of the interior and located top and bottom the core first plugs on the far drivers side f the core. Hence the cold air to the driver. I have flushed, almost every time I do one and multiple times and using compressed air to blow through the disconnected lines in the engine compartment. I NEVER HAVE HAD SUCCESS!!! But the cores are such a PIA I can hope.
This core is from My personal 04 VDP I just did in my shop at home. Cut it open so all can see a visual. This was AFTER flushing and blowing it out. The book time on the replacement is 5.50 hours without diagnosis, or flushing. Have Never beaten r gotten close to this time as the little clamps and O rings to seal someone should be shot over. They always leak if you just try the orings first. So I have learned that its best to smear some RTV generously around the orings and seal the lines with the STUPID clamps(can you tell I don't like them )
Let it sit overnight to cure. Fill the cooling system, purge air and run to operation temps with reservoir capped. Watch the connections for leakage. If it does redo it all. Yay!!!
If no leaks then put the blower housing back in place and finish the job.

 

Agree about the clamps, I replaced the phillips head clamp bolts with allen key head bolts that were a little longer, made it much easier to get the bolts started and tightened up.


Stu