In turbomachinery, labyrinth seals are key components to reach high performance of the engine. To that end, manufacturers of sealing systems tend to reduce the radial clearance between stationary and rotating parts of the turbine to increase efficiency. They also reduce the thickness of structural parts to get lighter designs. These new designs could lead to aeroelastic instability issues. To prevent such instability problems, an accurate prediction of the aeroelastic effective damping is necessary. Stability criteria used in the industry are mainly based on empirical observations and show limitations. A more representative prediction can be done using CFD calculations, but it remains computationally expensive. In this paper, a semi-analytical model is developed to analyze the fluid-structure interaction inside a multi-fins straight labyrinth seal. Fluid equations are written using a one control-volume bulk flow model, and assuming temperature fluctuations. This last feature is rarely addressed in the literature and is expected to provide better fidelity.