Ok, what i'd do now.
Check both the new & old stats are 82 C and they open and close, put
them in a pan of boiling water and use pliers to lift out and you'll see
them open and then shut as they cool.
Once checked if the new one is okay re fit it, fill up your system and
run the engine with the rad cap off, top up the rad to the filler neck,
once the engine gets to normal temp the stat will open, pop the heater
on full hot and top up the rad as the air comes out.
Once the rad stops popping out air check the heater is nice and hot,
keep checking the temp gauge on the dash while bringing the engine
up to temp.
Pop the rad cap on and fill the expansion tank to the max level, check
this once the engine has cooled as it should drop as the coolant is drawn back into the rad.
Once cool take the rad cap off and check the rad is full
Keep an eye on the temp gauge during this process and if everything
is okay it shouldn't overheat while you do this