The possibility that contact between the carbon-rich and hydrogen-rich layers may account for the existence of peculiar red giants is investigated by analyzing nucleosynthesis during high-temperature helium burning in convective regions in the framework of a simple one-zone model. It is found that the F-18 deposited in the intershell region by the hydrogen shell may be transformed into Ne-21 by alpha capture or into 0-18 by beta decay during the helium flash. The results indicate that the energy generation rate is significantly enhanced by F-18 burning and that the entropy of the convective zone may be increased enough to extend that zone. However, it is noted that contact with the hydrogen shell is possible only if the entropy of the convective zone equals that of the shell. The validity of the one-zone assumption is discussed.