Nope. After I drained and flushed with water, I filled to cover the tubes in the radiator, and added a little in the tank.. With the heat on and the engine running I continued to monitor the fluid level. Every time it dropped from air being expelled, I added more fluid to cover the tubes.When you say you ran it hot with the cap off, I assume you are talking about the pressure cap on the overflow tank / de-gas bottle?
After the level stabilized, I put the cap on, and left the cap off the tank and with the heat still on, shot down the road a couple miles and back. Because there was no pressure in the tank, it was safe to remove the radiator cap again to check the level.
Added more fluid and let it idle some more all the while the heat was on. I finally shut it off, filled the radiator to the tippy top put the cap on, filled the tank and drove it a couple days. I think I had to add some more to the tank, but that was it.
It helped it was a hot day, so the thermostat stayed open.