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Terahertz quantum cascade-lasers (QCLs) are able to produce higher optical output power at higher temperatures when operated in pulsed mode. Predicting a laser's behavior under pulsed operation in order to achieve performance requirements is, however, a nontrivial exercise: the complex and nonlinear interplay between current, electric field, and thermal transients gives rise to complex responses in both optical output power and emission frequency. In applications where it is important to predict and control these behaviors, establishing the link between current drive, emission frequency, and optical output power is necessary. In this paper, we demonstrate, via a realistic laser-specific model, that by appropriate manipulation of the drive pulse we can not only obtain a higher optical output at increased operating temperature but also both extend and linearize a QCL's frequency sweep. We suggest that consideration of laser behavior through realistic and comprehensive modeling is not only useful but is also required in any pulsed application in which emission frequency change is likely to affect performance.