Aims. We develop a simple model of coagulated dust particles of two sizes (3.5 and 60 nm radius) to understand the nature and the effects of coagulation, which could explain the evolution of the far-infrared (FIR) dust opacity observed in the transition between the diffuse and the dense interstellar medium (ISM) (nH > 103 cm-3). Methods. Using the discrete-dipole approximation (DDA) method, we have calculated the absorption coefficient, directly proportional to the opacity, of coagulated grains with varying numbers of sub-grains and of different grain composition. Results. We show that, in the transition from diffuse to dense clouds, an increase in the FIR opacity by a factor of about 2.7 is possible and a decrease in the grain temperature by up to 3−4 K can be explained by the presence of coagulated aggregates composed of four big grains and 4000 very small grains (40% of the volume of the BGs). The coagulation of very small grains into the aggregates leads to a decrease in the 60 μm emission. Conclusions. This model can explain the observed increase in opacity at long wavelengths, the decrease in temperature from the diffuse ISM to denser regions with the coagulation of grains into aggregates and the absence of the 60 μm emission with the coagulation of very small grains onto the surface of the big grains.