Motivated by recent theoretical arguments that expanding strings can be regarded as having a temperature that is inversely proportional to the proper time, tau, we investigate the consequences of adding a term proportional to 1/tau to the string tension in the Lund string-hadronization model. The lattice value for the tension, kappa0 ~ 0.18 GeV^2 ~ 0.9 GeV/fm, is then interpreted as the late-time/equilibrium limit. A generic prediction of this type of model is that early string breaks should be associated with higher strangeness (and baryon) fractions and higher fragmentation <pT> values. It should be possible to use archival ee data sets to provide model-independent constraints on this type of scenario, and we propose a few simple key measurements to do so.
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