Although the conductance variation vs. voltage is the dominant factor, the dielectric permittivity also varies, as is the case with most ceramics.Afaik, it is the parasitic resistance, not capacitance, between heater and cathode that can be varied by dc elevation - the capacitance remains constant.
It also varies with frequency, which is well documented.
Since capacitance effects at 60 (or 50) Hz are generally negligible, the voltage coefficient is not well documented, just mentioned in passing.