A number of theoretical and observational considerations suggest that coronal loops are bundles of unresolved, impulsively heated strands. This ``nanoflare'' model, as it is sometimes called, predicts high-speed evaporative upflows, which might be revealed as nonthermal broadening of spectral line profiles. We have therefore generated synthetic line profile observations based on one-dimensional hydrodynamic simulations for comparison with actual observations. The predicted profiles for Ne VIII (770.4 Å), a transition region line, and Mg X (624.9 Å), a warm coronal line, have modest broadening that agrees well with existing observations. The predicted profiles for Fe XVII (254.87 Å), a hot line that will be observed by the Extreme Ultraviolet Imaging Spectrometer (EIS) on the Solar-B mission, are somewhat broader and are also consistent with the limited number of hot line observations that are currently available. Moreover, depending on the properties of the assumed nanoflare and other parameters of the simulation, the Fe XVII profile can have distinctive enhancements in the line wing. This indicates a powerful diagnostic capability that can be exploited once Solar-B is launched.