This is my experience doing this:
If you don't invert your donor tank to get liquid, you will get very little CO2 to transfer, even if your destination tank is colder. Don't even waste your time trying. You have to either invert your donor tank or use a dip-tube tank.
If you invert the source tank, your destination tank will get about half full the first time. Putting it in the freezer ahead of time doesn't work that well, because the empty tank by itself just doesn't absorb much heat.
If you then freeze the half-full tank and reiterate the process later, it will actually be possible to over-fill on the second iteration, so be careful. If you put an over-full tank in your kegerator, it might be ok. If you put it out in room temperature or outside, the burst disk very well may blow.
At warm temperatures, there stops being liquid in a 10LB donor tank when there's still nearly 2 pounds of CO2 left, so it's pretty inefficient to do this for your sole setup.