We calculated a grid of evolutionary models for white dwarfs with helium cores (He-WDs) and investigated the occurrence of hydrogen-shell flashes due to unstable hydrogen burning via CNO cycling. Our calculations show that such thermal instabilities are restricted to a certain mass range (M=0.21...0.30Msun), consistent with earlier studies. Models within this mass range undergo the more hydrogen shell flashes the less massive they are. This is caused by the strong dependence of the envelope mass on the white dwarf core mass. The maximum luminosities from hydrogen burning during the flashes are of the order of 10^5 Lsun. Because of the development of a pulse-driven convection zone whose upper boundary temporarily reaches the surface layers, the envelopes hydrogen content decreases by Delta(X)=0.06 per flash. Our study further shows that an additional high mass-loss episode during a flash-driven Roche lobe overflow to the white dwarfs companion does not affect the final cooling behaviour of the models. Independent of hydrogen shell flashes the evolution along the final white dwarf cooling branch is determined by hydrogen burning via pp-reactions down to effective temperatures as low as 8000 K.
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