The stock GM cooling system even on todays standards is way over built...
U have new radiator, pump, clutch and stock fan with shroud...and new hoses...Correct?
I gather your symtoms are its ok while moving and gets hot idling correct?
No has nothing to do with thermostat, and if take it out without a restrictor it will run hotter....
In saying that , a faulty thermostat will cause your symptoms.
Buy a new one any way...a GM 180 deg, correct for the application...and test before install, dont assume it is ok....
electric jug water, hang the thermostat in it cold and heat it up, with a thermometer for when is open.
While at it, do the same with the temp gauge sensor, start cold, ground the body, then u can relate the postions of your gauge needle to real temps....And varify temps
Generally moving ok and idle gets hot is blocked/ restricted cores, and/ or no shroud...and a rare long shot, the impeller in the water pump has spun on the splines.
There are a coupe things that can make ppl think its getting hot when they stop at an interesection...
Partuarly noticable after a highway run the hit the intersection and the needle climbs.....if u increase rpms to a fast idle temp drops... that is normal....it will also drop if u sit there longer....what happens is there is a lot of heat in the block/heads, then water pump suddenly goes at a slow speed leaving water in a hot block to gert very hot... this eventually moves past the temp sensor, gauge goes up, into the radator cools and takes a while to get all the open road heat out
Thats normal
The other is over filling the raditor, again usually after a run, and spews the access water all over the ground... dont over fill the radiator....both of these can be and often are combined.
A not on temp guns...most people dont read the instructions, assume that simply aiming at a particular surface will give correct reading... this in NOT the case... cant beat a good old fashioned bi metalic probe or a bit of mercury.