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Increasing shares of fluctuating renewable energy sources induce higher and higher power flow variability at the transmission level. The question arises as to what extent existing networks can absorb additional fluctuating power injection without exceeding thermal limits. At the same time, the resulting power flow characteristics call for revisiting classical approaches to line temperature prediction. This paper presents a probabilistic modeling and simulation methodology for estimating the occurrence of critical line temperatures in the presence of fluctuating power flows. Cumbersome integration of the dynamic thermal equations at each Monte Carlo simulation trial is sped up by a specific algorithm that makes use of a variance reduction technique adapted from the telecommunications field. The substantial reduction in computational time allows estimations closer to real time, relevant to short-term operational assessments. A case study performed on a single line model provides fundamental insights into the probability of hitting critical line temperatures under given power flow fluctuations. A transmission system application shows how the proposed method can be used for a fast, yet accurate operational assessment.