It's not that expensive to put a new radiator and clutch fan in! Way cheaper than a new motor. And to help burp the air in the system is to put some sort of T connector that you can open the T part at the heater core lines! Just open the valve to burp out the air that gets trapped in those lines! One of the anti-freeze companies makes a kit that pops into the lines and it has a cap that you take off and hook up a garden hose to it, so in theory your filling the radiator from the heater lines! Which is the highest point of the cooling system!
Toyota's are notorious for taking forever to burp the air out of the system! Park on a very steep hill has been suggested many times!
Another idea, is how many miles are on the motor? When you put in the t-stat, what did the surface of the inside cooling surface look like? Did it have a grayish clay look to it?
