Accurate knowledge and control of thermal conductivities is central for the efficient design of heat storage and transfer devices working with deep eutectic solvents (DESs). The addition of water is a straightforward and cost-efficient way of tuning many properties of DESs. In this work, the thermal conductivities of aqueous solutions of reline, ethaline, and glyceline are reported for the first time. The non-equilibrium molecular dynamics Müller-Plathe (MP) method was used, along with the well-established GAFF and SPC/E force fields for DESs and water, respectively. We show that thermal conductivities of neat DESs are in excellent agreement with available experimental data. The addition of 25 wt% water results in nearly 2 times higher thermal conductivities in all DESs. A further increase in the fraction of water to 75 wt%, causes an increase in the thermal conductivities of DESs ca. 3 times. This behaviour is mainly due to the change in the microscopic structure of the DESs (i.e. hydrogen bonding) upon the addition of water. Our simulations reveal that thermal conductivities of aqueous DESs do not significantly depend on temperature. We also show that thermal conductivities strongly depend on system-size. System-sizes bigger larger than ca. 5 nm should be used.