Romanenko, A. JACoW Geneva, Switzerland The talk will report recent experimental results and theoretical understanding of the magnetic flux expulsion during cooldown provided by large thermal gradients. The complete expulsion of the magnetic flux can lead to record-high Qs at accelerating gradients of ~20 MV/m. High Qs were achieved in ambient magnetic fields up to 190 mG. These findings open up a way to ultra-high quality factors at low temperatures and show an alternative to the sophisticated magnetic shielding implemented in modern superconducting accelerators.