Rotating rolls are used to distribute liquids onto papers or other materials in order to coat their surfaces with thin films for further technical applications of the composed materials. In this contribution a numerical method is applied which solves the momentum balance in the liquid phase with the support of the Finite Element Method (FEM), taking free surfaces into consideration. The coupled equations of momentum and energy are solved on the basis of the Boundary Element Method (BEM). The process parameters are summarized in the friction number, the capillary number, the Reynolds number; the Stokes number and several ratios of the linear dimensions. Their influence on the fields of pressure, velocity, tension, and temperature is investigated and displayed graphically. A temperature gradient superimposed to the flow through the gap between the roll surfaces results in an additional influence on the velocity field and the coating thickness. The results of the numerical calculations are approximated by rather simple empirical equations.