Thermal lattice Boltzmann simulations are prone to severe numerical instabilities. While octagonal velocity lattices increase the range of temperatures that can be successfully simulated, the ranges are insufficient for many applications. Second order interpolation is required to correlate diagonal streaming to the square spatial grid. Here, the role of energy-dependent octagonal lattices is examined, an idea spawned from Gauss–Hermite quadratures. A nontrivial allocation scheme is now required to ensure moment conservation in connecting to the spatial grid. For the energy-dependent lattices, it is shown that there are no lower bounds to the temperature, thus allowing for higher Reynolds number simulations. Simulations are presented and compared to theory (viscosity and sound speed dependence on temperature) showing excellent agreement.