OK, so with out anti Freeze, you are spot on, you will find that the temp. will go down with anti freeze.

When bleeding, put a big dish under the car, you catch up the bleeding fluid and just put it back, no problem, so do not be shy to fill it with anti freeze.
Remember to drain all the water, Then fill with the right STRONG mixture of anti freeze, otherwise you will have it too diluted, and it will not help.
Then you have to start the bleeding all over again. These modern cars can not run without Anti Freeze.
Have fun
Herman