If you don't have an exhaust gas temp probe yet, get one. This allows you to monitor the EGT temps. When you pull in from a drive, you need to wait till this number drops to <350*. When towing, keep it under 1300*.
See my post here on the EGT probe install:
Installed my EGT probe and CTS today
I bought the one from Insight to make sure it would work with the gauges (I have a CTS). I didn't buy the expandable version but you can. Mount it in the back of the drivers side exhaust manifold.
Need to monitor ECT (engine coolant temp), EOT (engine oil temp) and EGT at the very least. These will allow you to tell if you have an oil cooler failure or getting close. You have to get the operating temps up to normal (EOT ~195), then drive between 55-65 on flat ground for 10 mins or so, steady speed, no passing, etc. While doing this, if you ever see your EOT get above 15* higher than your ECT your oil cooler is failing.
Transmission temp. Monitoring this will surely lengthen the life of your transmission. Typical "running around" unloaded and not towing you may get as high as 165°F. While towing, you might see 185°F. Fords long term upper limit is 250°F.
I also monitor my boost.
Here is a helpful link of things to monitor:
Budget 6.0L Build - Diesel Forum - TheDieselStop.com
So right now I'm monitoring EGT, ECT, EOT, Tranny temp and Boost.
2005 CCSB 4x4 6.0L Harley
8" ProComp lift, 20" Rockstars, 37" Nittos, Fox Reservoir Shocks, Dual Fox stabilizers, 2008 Tailgate with camera, 4" Straight Piped (no muffs, no kitties), Nerfs, Lights, X3 tuned by IDP, CTS, Optima Red Tops, Line-X, AutoPage