The effective population size (N_e) is a major factor determining allele frequency changes in natural and experimental populations. Temporal methods provide a powerful and simple approach to estimate short-term N_e. They use allele frequency shifts between temporal samples to calculate the standardized variance, which is directly related to N_e. Here we focus on experimental evolution studies that often rely on repeated sequencing of samples in pools (Pool-seq). Pool-seq is cost-effective and often outperforms individual-based sequencing in estimating allele frequencies, but it is associated with atypical sampling properties: Additional to sampling individuals, sequencing DNA in pools leads to a second round of sampling, which increases the variance of allele frequency estimates. We propose a new estimator of N_e, which relies on allele frequency changes in temporal data and corrects for the variance in both sampling steps. In simulations, we obtain accurate N_e estimates, as long as the drift variance is not too small compared to the sampling and sequencing variance. In addition to genome-wide N_e estimates, we extend our method using a recursive partitioning approach to estimate N_e locally along the chromosome. Since the type I error is controlled, our method permits the identification of genomic regions that differ significantly in their N_e estimates. We present an application to Pool-seq data from experimental evolution with Drosophila and provide recommendations for whole-genome data. The estimator is computationally efficient and available as an R package at https://github.com/ThomasTaus/Nest.