Nights,
Do exactly as Chris has told you. If the car is cold, there is no danger of exploding hot antifreeze. Just take the cap off, turn the car and let it idle. You won't have to worry about antifreeze bubbling out unless you are really goosing the throttle to speed the process up, which by the way I would NOT recommend doing from under the hood if you aren't really familiar with this process.
Also, trust me, I have 2 83's, you can't get the nose up in the air too high.
I have a very steep drive and I usually point it nose up put chocks behind the rear wheels and then jack the front end up with my shop jack another 3 foot and then use a ladder to be able to see into the radiator.
The only time you should see any bubbling of the antifreeze is when an air bubble is coming out. Some times really big pockets of air can surprise you.
If you have an air bubble trapped on the back side of the T-stat, you will most likely get no reading from the temp sending unit even if it is plugged in properly. The unit can't read air temp, it can only read liquid.
When you put the thermostat in, you did make sure to put it right side up? In other words, the diddle valve is straight up and not down or on the sides is it? If so, it will be almost impossible to get all the air burped out. Also did you cut the diddle valve off and drill out the hole a little bit? That makes it much easier to get the system to fully burp.
Just be patient and as Chris already said, make sure you have the windows down or the doors open and the heater set to blow at highest heat and high speed fan. Depending upon your altitude, this can take awhile. I live just over 6.000 ft. and it takes me well over an hour to burp the system after a coolant or T-stat change.
Remember not to have any pets around while you are doing this as antifreeze tastes very sweet to them but is deadly.
HTH
Leslie