Sounds when you tightened down the t-stat, you opened it up slightly since it was the wrong part, so it's always flowing coolant even when cold. This would 100% explain your issue. I would not do the cardboard thing, just get the right t-stat for it.

 

I have the same problem, but mine has the correct thermostat. I changed it thinking it was stuck open but the old one was fine. In 40° weather, idling for 30 minutes, it will only get to ~175°. Driving it will be at 180 - 185, the quarter mark on guage, after 30 miles of diving. I just deal with it.

 

Oh yeah, and I take the fan off during the winter.

 

Are you having heater trouble? The gauges in these trucks are known to be inacurate.

 

Me? No. Heater works fine, but on those 20° mornings, it stays quite chilly in the cab. When it's 65 or above, it'll warm up to normal operating temperature. This is with two different clusters that read the same thing as far as temp goes. My trans temp on cluster(denali) doesn't move on really cold mornings.

Sorry to thread jack OP.