Beetles of the genus Melanophila acuminata detect forest fires from distances as far as 130 km with infrared-sensing organs. Inspired by this extremely sensitive biological device, we are developing an IR sensor that operates at ambient temperature using MEMS technology. The sensor consists of two liquid-filled chambers that are connected by a micro-fluidic system. Absorption of IR radiation by one of these chambers leads to heating and expansion of a liquid. The increasing pressure deflects a membrane covered by one electrode of a plate capacitor. The micro-fluidic system and the second chamber represent a fluidic low-pass filter, preventing slow, but large pressure changes. However, the strong frequency dependence of the filter demands a precise characterization of its properties. Here, we present a theoretical model that describes the frequency-dependent response of the sensor based on material properties and geometrical dimensions. Our model is divided into four distinct parts that address different aspects of the sensor. The model describes the frequency-dependent behaviour of the fluidic filter and a thermal low-pass filter as well as saturation effects at low frequencies. This model allows the calculation of optimal design parameters, and thereby provides the foundation for the development of such a sensor.