The earth-to-air heat exchanger (EAHE) is a low-energy device used to improve the thermal condition of buildings, which is filled with the air directed from the outside and surrounded by the soil. The temperatures of both the air and soil are periodically fluctuating, leading to the EAHEs working in a harmonic thermal environment. However, most of the previous theoretical studies investigated the performance of EAHEs by ways of static and steady-state models, paying insufficient attention to the temperature phase shifting and fluctuation attenuation effects. The main purpose of this work is to develop an approach to predict the performance of EAHE subjected to harmonic thermal environments. The harmonic temperature signals transmitted from both the pipe inlet and the ground surface are incorporated in the model by means of the 'excess fluctuating temperature'. The amplitude dampening and phase shifting of the EAHE air temperature for both annually and daily fluctuating cycles are derived as explicit expressions. The analytical results are validated against numerical simulations. The model is applied in a hot-summer/cold-winter region. Results indicate that a deep-buried EAHE pipe can reduce the air temperature by 7 degrees C on a summer day. The maximum cooling or heating capacities occur in spring/summer or autumn/winter transitional seasons. The use of an EAHE pipe can create a 3000-W cooling or heating capacity. (C) 2015 Elsevier Ltd. All rights reserved.