I read this online, so if you put them in a hot shed for the summer, I think you will be safe:
Myth 3: Bedbugs can typically live a year without a meal
Scientists debate this point, but evidence suggests that at normal room temperature, about 23 degrees Celsius, bedbugs can only survive two to three months without a blood meal. But because they are cold-blooded, their metabolism will slow down in chillier climates, and the insects may live up to a year without feeding.
http://www.scientificamerican.com/ar...bout-bed-bugs/