The flight instructor reported that she and the student pilot checked the weather conditions prior to departing on an instructional flight, and noted thunderstorms were forecast for the area about 1 hour after their flight was scheduled to be completed. While returning from the flight as scheduled, the flight instructor noted thunderstorm activity to the northwest and strong winds at an airport located about 15 miles north of their destination airport. While on final approach to land on runway 30, the flight instructor noted that the reported winds were from 260 degrees at 10 knots. She continued the approach normally; however, during the landing flare a significant change in headwind caused the airplane to climb. The flight instructor added engine power and pitched up, with the intention of aborting the landing; however, the airplane quickly descended uncontrollably onto the runway. The airplane landed hard and sustained substantial damage to the left wing. Review of weather radar around the time of the accident revealed a line of approaching echos, with a defined gust front ahead of the system. Winds reported at a nearby airport, about 30 minutes before the accident were from 210 degrees at 10 knots, and from 300 degrees at 18 knots, gusting to 29 knots, about 30 minutes after the accident.