If its getting warm in under a mile you have a problem.
As an indication I used to work 12 miles way, new stat fitted thought shes running a tadge hot, same on the way home, removed stat it was stuck shut! so it had no rad cooling for 24 miles and still ran fine, so if you are getting hot in 1 maybe 2 something else is going on.
Plius as yo u still have the viscous fan fitted Im amazed it ever gets warm enough to open the stat!
As for stats failing shut Im not saying it doesnt happen but Ive not personally seen it with my own eyes, modern **** maybe, but not these old clunkers.
Both my tdi engined cars take roughly the same time to heat up etc, both are fitted with Tim capilliary gauges from ebay, very accurate.