Is it possible that EGR has been removed and/or blanked off? If so then the EGR coolant feed would be blanked too. Removing the clamp allows coolant to flow to the radiator but it's not being heated by the EGR and thus leads to lower temp and slower heating up?The SSP 467 on the V8 TDI and also the Erwin manual section on the engine provide lots of details to understand what's going on. From a quick look it appears the electric pump in question is dedicated to the EGR cooler. I am not sure if there is a second electric pump somewhere for the internal cabin heater and transmission heating / cooling or whether these circuits come off the main pump or the EGR pump. The are lots of valves and a couple of thermostats at least that control how these circuits work. It would take me about 4 hours to figure it out with the manuals in hand and going over the actual piping circuits on the engine, i hope I never need to do it .
I suspect most mechanics ( VW dealer or independent) would take even longer to figure it out to diagnose your problem better, if they could be bothered which is probably why the clamp bodge fix.