We introduce a novel method to determine cost-optimized Active Power Curtailment (APC) of Renewable Energy Sources (RES) considering weather dependent Dynamic Line Rating (DLR). A new formulation of the Security-Constrained Optimal Power Flow (SC-OPF) is developed and applied in a case study. We demonstrate the reduction of the required preventive APC in the (N -0) case for (N -1) secure grid operation due to the consideration of thermal inertia of overhead power lines. Considering thermal inertia allows relying on curative APC that is activated only after an (N -1) situation occurs. The overhead power line temperature, calculated with the temperature dependent power flow, acts as a new limit for line loading and releases unused transmission reserves. The power system can be utilized to a greater extent, with a reduced demand for congestion management.