As said, a 3 mile drive from a cold started engine, especially with a diesel engine, is not going to give real good MPG's. Diesel engines have a lot of mass compared to a gas engine and it take a lot longer to heat up from cold. You will see the difference real quick when you drive longer distances per trip. Short travel to work is a passing thing as you are retiring soon anyway.
Compared to your 5.3 gas engined much lighter truck for instance, you will see a little less MPG on the short trips from cold but higher MPG's than the 5.3 gas truck on longer mostly highway trips. It will balance out with the nod going to the diesel. Really comes vividly to light when comparing the same RV unit towing MPG's between the 2 trucks (5.3 gas and the 6.6 diesel). Climbing grades and higher altitude driving will really brighten up your travel like the difference between night and day. Then adding in the fact that your diesel truck weighs that 1 to 1-1/2 tons more than your little 5.3 gas truck did and it always takes more "energy" to move the extra weight, you will have a smile on your face that just won't go away! It's a condition known as a "Perma-grin"!
You also need to check the size of the tires on the truck as 245/75/16 "E" was the OEM size when new. Many including us have gone to 265/75/16 "E" and that is a larger diameter and wider tire so it turns less times during a mile of travel which means lower indicated MPG's on the DIC. This gives the perception of less MGPs but is not accurate. Also whether the tires have full tread depth or are worn down plus the air PSI in the tires alters the distance the tire travels in each revolution. These factors can make up to nearly 1 mpg difference between DIC indicated MPG's and hand calculated MPG numbers. Hand calculated has to be done over several fillups to be reasonably accurate.
