It depends, with ReRAM the ion mobility in the dielectric layer can be tuned, lower mobility means a higher voltage is required across the cell for filament growth but a lower thermal dependence.
the problem is the material properties link power and variability. This means that you either get good variability or higher power consumption, but never good variability at low power at the same time
That's partially true, there are other tradeoffs that can be made to optimise power and thermal dependence at the cost of something else but both specific use case and fab availability/reliability need to be factored in.