The parametric sensitivity behavior of a tubular reactor with co-current external cooling is investigated using a generalized parametric sensitivity criterion. This criterion is based on the occurrence of a maximum value for the normalized sensitivity of the hot-spot with respect to any of the input parameters of the reactor. Comparisons are made with the Adler and Enig criterion, which is based on geometric feature of the temperature profile; this criterion is shown to give qualitatively erroneous results in some cases. The regions of parametric sensitivity in the reactor parameter space are also reported for various values of the involved dimensionless parameters.