Enhanced plasma heat conductivity in the presence of kinetic Alfvén waves (KAW) is predicted theoretically. The enhancement is shown to be strongest when the electron collision frequency exceeds the particle transit frequency in the wave field. Alfvén waves (both KAW and ideal MHD Alfvén eigenmodes generating the KAW) are studied in a shot of the Wendelstein 7-AS stellarator. On the basis of these results, strong thermal crashes observed during bursting Alfvénic activity in the mentioned shot are explained.