N.H. Rev. Stat. Ann. § 4:5

In case of the temporary inability, by reason of illness or otherwise, of the head of any state department to perform his duties, where the law does not designate or make other provision for the appointment of an officer to perform such duties, the governor, with the advice and consent of the council, may appoint a person to act in his stead, and the person thus appointed shall have the powers and perform the duties of such head of department for such time, for such compensation, and subject to such qualifications as the governor and council may from time to time deem expedient.