The paper develops an optimization method for assessing transmission network vulnerability to small changes in generation (as caused, for example, by wind forecast inaccuracy). The method computes the smallest deviation (in a weighted 2-norm sense) from the nominal generation pattern that would drive a particular line to a specified temperature, over a given time horizon. The 2-norm weighting matrix provides a means of capturing spatial and temporal coupling between generation sites and time intervals. The temperature constraint is second-order in voltage angle differences. The problem is therefore a quadratically-constrained quadratic program (QCQP). Solving the QCQP for each line in the network yields a set of candidate generation deviation patterns which may then be sorted to determine the lines that are most vulnerable to overloading. The paper develops a computationally efficient algorithm for solving this QCQP. An example explores line-overload vulnerability due to changes in wind patterns. Numerical results emphasize the framework's ability to incorporate evolving ambient and system conditions, as well as computational scaling properties.