04 Chev. Avalanche 1500 Z71 5.3 125K mi. Temp gauge reads erratic from 210 to 245 or so. heat blows warm then cold. Coolant level, OK. I have been told could be sticky thermostat but usually is restricted heater core. Was advised to switch incoming and outgoing hoses to the heater core to attempt to back flush? What do you suggest?

Honestly bro...been there done that. Time for a new radiator. Ur gonna spend a good chunk of change replacing everythng u can thnk of. I did da same. Process of elimination left the radiator. THEY DO NEED REPLACING. Replaced mine around 200000 miles along and fuel pump twice both got about 150000 miles. Ol faithful rollin wit 347000 now.

Normally the engine operates at 195F, if you did not replaced thermostat with another one at 185F. If the temperature has a tendency to rise up, the reason is a partially obstructed cooling system or/and a bad thermostat.
The first part of the cooling system that gives up is the heater core, because the coolant flowing channels are thin. You got a good advice but not the best one. It is the time for a coolant flush in your car. To do do it right then you need time. Plan ahead for a week end. With a cooled engine, start as your friend advised you with the heater core hoses. Disconnect both of them, but the dirt has to go out of your car, so with a garden hose back flush it and let the dirt to get out of your cooling system. After you will get clean discharge, it is the time for coolant bottle, remove it, discharge the used coolant and clean it. The third to come is the radiator. Open the drain cook, or disconnect the lower radiator hose, and disposal used coolant properly. Now open the radiator cap and flush with water the radiator till discharge will be clear. You think that you are done? Not yet. There is half of old dirty coolant trapped in the system.
Install everything, and connect all coolant system hoses, radiator, heater core and coolant bottle. Now you have to run your car with water. Fill out the cooling system with distilled water, start engine, turn on the heater high, and run till upper radiator hose get hot. That means the thermostat opens.
Let the engine to cool down, open the radiator cap, and draining cook or lover radiator hose and drain everything. You can use flush detergent if you wanted at this stage, but flushing with detergent will add 4 more hours, because detergent is colorless and you have to guess how many fill and drain processes do do to get rid of it. I do not do it, but if your cooling system is very dirty you have to do it. After the last drain, fill the cooling system with concentrated antifreeze and 30% distilled water. The reason is because it is more water trapped inside the cooling system. The goal is to reach 50/50 concentration. You need a coolant tester to find this. Start the engine and add coolant til radiator is full. Install the radiator cap and bleed the system. After driving you car for a day or so, let engine to cool down, open the radiator cap check the concentration of coolant with the tester and add antifreeze or distilled water as necessary. It is a good idea to replace the thermostat while flushing the radiator. This procedure has to be done every 2 to 3 years. It is up to you to decide to use RED GM Dex-Cool or GREEN Prestone antifreeze.
In all my cars I have replaced Dex-Cool with Prestone, but I flush the system every 2 years, and I never had a cooling system problem in all my cars.

Thats way too warm.....when it gets that hot.the tranny and tranny fluid in the radiator heat up also. i went thru the exact same thing. 03 avalanche 276000 miles. just recently started changed all the basics...w pump, thermostat, fan clutch. all to no avail until i replaced the radiator. runs perfect now. I guarantee everyone out there that has a similar problem that this is the cure.