Is your radiator a "honycomb" style?
I was told those style couldnt be "rodded out" or cleaned.
So...what they do is keep your top and bottom tanks and re-core the actual radiator portion.
As far as running without a thermostat,,NOT GOOD!! Your coolant moves thru so fast it doesnt have time to be cooled by the radiator. The thermostat slows it down so it has time to let the radiator do its job.
Marty