Owing to its longevity and extremely high information density, DNA has emerged as an attractive medium for archival data storage. Scalable parallel random access of information is a desirable property of any storage system. For DNA-based storage systems, however, this yet has to be robustly established. Here we develop thermoconfined PCR, a novel method that enables multiplexed, repeated random access of compartmentalized DNA files. Our strategy is based on stable localization of biotin-functionalized oligonucleotides inside microcapsules with temperature-dependent membrane permeability. At low temperatures, microcapsules are permeable to enzymes, primers, and amplified products, while at high temperatures membrane collapse prevents molecular crosstalk during amplification. We demonstrate that our platform outperforms non-compartmentalized DNA storage with respect to repeated random access and reducing amplification bias during multiplex PCR. Using fluorescent sorting, we additionally demonstrate sample pooling and data retrieval by barcoding of microcapsules. Our thermoresponsive microcapsule technology offers a scalable, sequence-agnostic approach for repeated random access of archival DNA files.