Yes, the dryer will kill bed bugs.

More Info: Washing your clothes in hot water and drying them on the highest setting will kill bed bugs.

Temperatures below 25°F will kill bedbugs.  You can use this to your advantage to kill bed bugs by placing small, infested items in a freezer bag and placing them in the freezer.  In the winter if the temperature drops below 25°F you can pull your mattress out of doors to kill the bed bugs.

If you have a bed bug infestation, you should consult a professional exterminator in conjunction with your in-home efforts to ensure that he eradicates the infestation and not just a few of the population.

What Are Bed Bugs?

Bed bugs are parasitic insects that feed on the blood of warm-blooded animals. The most common type, the species Cimex lectularius, consumes human blood when it is available. The mouthparts of the insect are used to pierce the skin. The name "bed bug" was coined due to the insect's tendency to infest beds where a sleeping host becomes an easy meal. Human symptoms of bed bug exposure may include skin irritation, and some psychological side effects.

How Do You Prevent Bed Bugs?

You can prevent bed bugs by taking precautions to keep bedding and bedroom areas clean and taking measures to reduce the risk of introducing the bugs into the home or on the clothing. First, clean bedding and clothing frequently.  Next, if coming home from a trip, all clothing should be washed immediately and luggage cleaned out as well. Bed bugs can easily hitch a ride and infest a home. You can also apply insecticide sprays around the home to prevent these bugs from getting in.