My last truck was a 2005 Chevy 3500 SRW - duramax/allison. I had the same temps - most of my towing was on the east coast. The fan clutch should kick in when pulling hills when the engine temps goes higher.
The allison tranny temp will "follow" outside air temp when it gets hot out. The dash gauges are not as accurate as a digital gauge.
I have an Edge CTS on my truck - tranny temps are the same as the DIC (digital). Engine temp is 20 degrees cooler on the Edge - dash gauge being analog is not as accurate.
I have the coolant flushed every 4 years. (per the manual - 5 years or 150,000 miles - Using coolant other than DEX-COOL may cause premature engine, heater core, radiator and fuel operated heater (van models only) corrosion. In addition, the engine coolant may require changing sooner, at 50 000 km (30,000 mi) or 24 months, whichever occurs first).
I use TranSynd in the tranny - synthetic and rated for higher temps and less oxidation when it gets hot (greater than 265 degrees)
Rotella T synthetic in the engine
Mobil 1 synthetic 75X90 in the front and rear diff.