The emergence of Large Language Models (LLMs) has transformed information access, with current LLMs also powering deep research systems that can generate comprehensive report-style answers, through planned iterative search, retrieval, and reasoning. Still, current deep research systems lack the geo-temporal capabilities that are essential for answering context-rich questions involving geographic and/or temporal constraints, frequently occurring in domains like public health, environmental science, or socio-economic analysis. This paper reports our vision towards next generation systems, identifying important technical, infrastructural, and evaluative challenges in integrating geo-temporal reasoning into deep research pipelines. We argue for augmenting retrieval and synthesis processes with the ability to handle geo-temporal constraints, supported by open and reproducible infrastructures and rigorous evaluation protocols. Our vision outlines a path towards more advanced and geo-temporally aware deep research systems, of potential impact to the future of AI-driven information access.