The successful design of biomass hydrothermal reactors could be substantially enhanced by computational fluid dynamics (CFD) simulations. However, their performance is still limited by the complexity of the involved physicochemical phenomena and the scarcity of experimental data. This study employs such simulations to analyze the thermo-fluid dynamics of an unstirred batch hydrothermal reactor. By assessing the reactor's response to a lateral heat source, we show that correctly including various phenomena, such as phase transfers and temperature-dependent properties, enables accurate reproduction of natural convection, providing a more solid base for CFD studies on hydrothermal units. The results provide valuable insights into the reactor's inner mixing, which for pure water appears adequate despite the absence of stirring. Additionally, we explore two approaches to include a biomass fixed bed or a non-Newtonian sludge. Discussing future efforts needed to make the simulation of such media more established, we show that their presence may indeed hinder mixing, with implications for the products' quality and safety and for hydrothermal processing control and design.