This paper presents a detailed analysis of the temporal transferability of heterogeneous overdispersion parameter negative binomial models for crash severity types in California. The Furnival-Wilson leaps and bounds algorithm was used to identify optimal safety performance function specifications. The overdispersion parameter was allowed to vary across roadway segments as a function of roadway geometrics. Sixty models were developed for five major severity outcomes for homogeneous roadway segments for each of the periods 2005 to 2010, 2011 to 2012, and 2005 to 2012. Model transferability tests were conducted with likelihood ratio tests, and it was determined that temporal transferability rates (from the 2005-2010 period to the 2011-2012 period) were poor. The findings indicate the potential time instability of safety performance function parameters. The analysis found a higher rate of transferability for rural safety performance functions compared with urban safety performance functions. The rate of transferability was highest for severe injury and fatal injury. This result shows that the role of the overdispersion parameter in the transferability of safety performance functions must be considered. The absence of information on changes in economic, environmental, vehicle fleet, and driver population data limits the specification of the overdispersion parameter to roadway geometrics. Although it is an improvement over the current practice of the use of a constant overdispersion parameter, economic, environmental, and vehicle-driver population data might be useful for improving model transferability over time. The implications are that safety analysis methods such as crash modification factors, network screening, and excess crash estimations must take into account parameter variability over time.