I've experienced a t/stat stuck closed before with very similar symptoms. The little 'jiggle valve' in it would allow enough flow at tickover, but not when running.
Your symptoms would indicate a partial blockage somewhere in the system, or something else limiting flow.
I think I'd start with Zeddo's theory, remove the rad and flush it.
If that doesn't cure it, then next I'd replace the t/stat.
If that doesn't cure it I'd start thinking about the water pump. Don't some have problems with vanes braking?
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