The Charge cooler is also a common
problem on these.
If this was my car as the one martix pipe is only getting warm slowly I'd go about it like this, although id be doing it myself.
Power flush the whole system disconnecting pipes as i went as described earlier.
Heater Matrix swapped out.
Bypass the charge cooler, really easy to do to rule that out. Or Bore scope
And only then would a look towards the EGR cooler. It could well be that but thats an expensive job unlike diagnosing the charge cooler. Any garage should have a bore scope to look for water in there.