The pilot of the helicopter reported that he had landed and was going to reposition to another company landing zone after dropping of his crew chief. The pilot opened the engine cowling to allow the engine to cool before restart. However, the pilot did not perform a thru flight walk around and climbed in to the cockpit and took off. About sixty seconds after departure, he felt a large thump throughout the airframe and landed as soon as practicable. Upon shutdown and inspection, he noticed that the engine cowling had departed the helicopter and struck the right two main rotor blades and the vertical stabilizer. Substantial damage was sustained to the right main rotor blades and the vertical stabilizer. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. In the recommendations section of the National Transportation Safety Board Pilot Aircraft Accident Report, the pilot specified that the company has issued a policy that prohibits opening the engine cowling for the sole purpose of allowing the engine to cool. Additionally, the policy directed a pre-takeoff helicopter inspection to be completed by a qualified technician.