Repeated cycles of internal pressure are a primary cause of cement sheath sealing failure during multi-stage fracturing. However, the influence of temperature on cement sheath performance, as well as the damage characteristics across different well sections, has not been adequately investigated. In this study, uniaxial compression experiments were conducted to obtain the compressive stress-strain curves of cement samples cured at different temperatures. A numerical model based on a plastic damage framework was developed. This model was used to investigate the compressive damage characteristics and cumulative plastic deformation of the cement sheath under cyclic internal pressure. The effects of cyclic pressure magnitude, number of cycles, and temperature on compressive damage and micro-annulus size were analyzed. Additionally, the micro-annulus dimensions were quantified. Furthermore, the impacts of well depth and casing eccentricity on cement sheath damage and micro-annulus growth were evaluated. The results show that the compressive strength of cement stone decreases significantly with increasing curing temperature. At room temperature, the strength is 57.35 MPa, dropping to 18.06 MPa at 140 degrees C. This decrease is accompanied by a notable reduction in elastic modulus. The compressive damage and micro-annulus size of cement sheaths become less sensitive to cyclic casing pressure and cycle number as the curing temperature increases. In vertical well sections, the amplitude of cyclic internal pressure increases with depth, resulting in greater damage and larger micro-annulus sizes. In horizontal well sections, damage and micro-annulus size increase progressively from the toe to the heel, with a significant rise observed during the first five cycles. Casing eccentricity in horizontal sections significantly exacerbates compressive damage and enlarges the micro-annulus, shifting the failure risk zone further towards the toe. An engineering case study was conducted to explore the distribution characteristics of the micro-annulus along the entire wellbore and to predict potential risk areas. The results indicate that micro-annulus size initially increases and then decreases with depth, high-pressure fracturing operations exceeding 120 MPa and casing eccentricity significantly enlarge the cement sheath failure risk zone, extending it from the toe toward shallower depths.