Renuka Majumdar (55) was killed when a tree branch hit her during the storm while she was returning home, the police said.
One Narayan Biswas (52) of Badkulla, died after the roof of a makeshift structure he was sitting in, collapsed. His relative Bijan Biswas was badly injured in the incident, the police said adding, the injured has been admitted to Shaktinagar hospital for treatment.
The day's highest temperature in West Bengal was recorded in Bankura at 42.2 deg C, which was closely followed by Burdwan (41 deg C), Asansol (40.1 deg C) and Sriniketan (40 deg C), the Met department said.