putting in a lower temp thermostat wont cure cooling issues. if the cooling system cant cool to a higher temp it sure wont cool to cooler temp.
take note if it overheats no matter what... or if it cools at cruising speed but will overheat at idle. thats a fan issue.
you replaced the radiator.... which means the cooling system was drained.
its very easy to get a huge air pocket in the engine.
i had overheating problems that turned out to be big air pockets in the cooling system.
best way to burp the system is jack the drivers side up real high to make the radiator cap the highest point in the cooling system. start the car up and let her warm up with the cap off. keep the radiator full and wait for the thermostat to open. if you get coolant puking out as the tstat is about to open. dont freak out and shut the car off. let it puke, its air bubbles trying to get out. i usually keep a bucket under the car and dump the spilled coolant right back in.
once the bubbles get out the coolant level should drop quickly. keep it full and i usually run it for another 10 mins or so and keep the rad full, then pop the cap back on and shut her off.