Summary Temporal boundary misalignment occurs when area boundaries shift across time (e.g., census tract boundaries change at each census year), complicating the modeling of temporal trends across space. Large area-level datasets with temporal boundary misalignment are becoming increasingly common in practice. The few existing approaches for temporally misaligned data do not account for correlation in spatial random effects over time. To overcome issues associated with temporal misalignment, we construct a geostatistical model for aggregate count data by assuming that an underlying continuous risk surface induces spatial correlation between areas. We implement the model within the framework of a generalized linear mixed model using radial basis splines. Using this approach, boundary misalignment becomes a nonissue. Additionally, this disease-mapping framework facilitates fast, easy model fitting by using a penalized quasilikelihood approximation to maximum likelihood estimation. We anticipate that the method will also be useful for large disease-mapping datasets for which fully Bayesian approaches are infeasible. We apply our method to assess socioeconomic trends in breast cancer incidence in Los Angeles between the periods 1988–1992 and 1998–2002.