Meteorological radar databases exist providing rain rate maps over areas with a sampling period of 2--15 min. Such two-dimensional, rain rate map time series would have wide application in the simulation of rain scatter and attenuation of millimeter-wave radio networks, if the sampling period were considerably shorter, i.e., of the order of 10 s or less. However, scanning a large radar at this rate is physically infeasible. This paper investigates a stochastic numerical method to interpolate point rain rate time series to shorter sampling periods while conserving the expected first- and second-order statistics. The proposed method should generally be applicable to the temporal interpolation of radar-derived rain rate maps. The method is based on the experimentally measured simple-scaling properties of log rain rate time series. It is tested against 9 gauge years of rapid response drop-counting rain gauge data, with a 10 s integration time, collected in the southern UK. The data are subsampled to yield time series with a 10 s rain rate measurement every 320, 640, and 1280 s. The subsampled time series are then interpolated back to a 10 s sample interval, and the first- and second-order statistics are compared with the original time series.