Where is the plug in for the block heater on a 2005 gmc sierra 2500?

SOURCE: 2007 gmc sierra 2500 IAT sensor

Well, the IAT (Intake Air Temperature) sensor is located on the air intake duct between the filter and the throttle body (Assuming you have the 6L motor). The wires are easily visible at the plug that connects the sensor to the wiring harness. That's the easiest place to access them.

SOURCE: Block Heater not working

There is no fuse on a block heater. It is an extension cord with a resistor (element) on the end (see photo. If it not working, the resistor (coil) has failed. A new block heater is required.
Before replacing, however, check the outlet and/or beaker the outlet is on to see if it has tripped.
I too live in s/e Michigan, and it was -19 this am. No block heater can keep up with these extreme temps.
:)

SOURCE: 2003 GMC Sierra heater Blower wont shut off

My 2003 Sierra's blower came on by itself in the garage while I was sleeping and ran the battery completely down. I had to replace the blower switch located under the glove box next to the blower at the bottom of the right corner of the dash. The switch is in front of the blower and held in by two screws. Disconnect the two wire connections. This is a "dealer only" part and cost me 65.00. Also check the wire harness with seven wires connected to it for melted plastic. It will be marked "ABCDEFG". If it has melted, you'll need to replace it. Pay attention when reinstalling either part, that the wires "ABCDEFG" match the switch in that order.

SOURCE: 2005 GMC Sierra Overheating

If your sure there is no trapped air in system after refill and air bleed off, is fan clutch pulling good air thru radiator? Even if it is, the heater should have coolant as hot as what temp gage is showing! Try backwards flushing heater core (dex cool is notorious for plugging these up). There is a TSB for cracked cylinder heads from GM for unexplained coolant loss.Remove drivers side valve cover, and look at center three head bolts for coolant around them, if coolant has been getting in thru this suspect area, there will be a milky/pudding like goo under valve cover and on head. GM had a company called Castec cast these and the areas near the head bolts were found to be too porous (NO recall YET!) Ya, you guessed it, replace heads! Unfortunately, if its gotten hot to many times, it has probably hurt the heads/gaskets. Hope this helps. PS: The castec logo is under the rearmost pair of rocker arms,may have to remove them to see.

SOURCE: 2005 gmc sierra 2500hd heated seat turns off

you have a couple of problems first of all your drivers sd=ide heated heat pad is probably faulty, for your heating problem you may have to get the hvac doors recalibrated.