Temporal disaggregation is a method commonly used in official statistics to enable high-frequency estimates of key economic indicators, such as gross domestic product (GDP). Traditionally, such methods have relied on only a couple of high-frequency indicator series to produce estimates. However, the prevalence of large, and increasing, volumes of administrative and alternative data-sources motivates the need for such methods to be adapted for high-dimensional settings. In this article, we propose a novel sparse temporal-disaggregation procedure and contrast this with the classical Chow-Lin method. We demonstrate the performance of our proposed method through simulation study, highlighting various advantages realised. We also explore its application to disaggregation of UK GDP data, demonstrating the method's ability to operate when the number of potential indicators is greater than the number of low-frequency observations.