Understanding processes leading to ultra-low and ultra-high thermal conductivity is essential to functional material design. For zinc phosphate (ZnO)_x(P₂O₅)_1−x glasses the competition between polymer-like phosphate chain length and zinc oxide networks rapidly influences the absolute values of thermal conductivity. Glass samples with a concentration of x = 0.6, where sizes of phosphate chains and zinc oxide networks are in balance and both have minimum sizes for the overall glassy matrix, the thermal conductivity reached a possible theoretical minimum value for solid-state materials of 0.1 W K⁻¹ m⁻¹ at 300 K. In these glasses, the structure can be simply tuned by changing the chemical concentration of zinc oxide x in a wide concentration region. Shifting the composition by ten molar percent below or four molar percent above x = 0.6 results in a rapid fourfold increase in the thermal conductivity to approximately 0.4 W K⁻¹ m⁻¹. The low-temperature properties provide additional information about the type of heat carrier and confirm the polymer-like character of the (ZnO)_x(P₂O₅)_1−x glasses.