Ok i tried to do it with some physics:
using this chart:
http://www.astro.sunysb.edu/mzingale/wdconvect/initial_model_sm.pngwe can assume that a white dwarf is on average, 5e8 Kelvins.
the formula for heat capacity of a degenerate electron gas is
Cv=pi^3/2*k^2*T*N/Ef
where k is the boltzman constant, T is the temperature, N is the number of electrons, and Ef is the fermi energy
T=5e8k
mass is 1e30kg (assuming white dwarf of about 0.5 sol masses for now)
assuming white dwarf is made of 100% carbon, which should be a sufficient estimate, and a carbon atom weighs about 12amu or 2e-23 grams which means 5e55 carbon atoms in out white dwarf. since each carbon atom has 6 electrons, that is 3e56 electrons in our white dwarf
N=3e56
to find fermi energy:
Ef=h-bar^2/2m*(3*pi^2*n)^2/3 where h-bar is dirac's constant, m is the mass of an electron, n is the density of electrons.
Density=1e9kg/cm=3e32 electrons/cm^3
n=3e35
dirac's constant=h/2*pi where h is planck's constant
m=9.1e-31 kg
Ef=6.603e-14 kg*m^-2*s^-2
Cv=pi^3/2*(1.38065×10^-23)^2*5e8*3e56/(6.603e-14)
Cv=6.713e33 j/kgK
He=6.6713e33mT joules, where He is heat energy, m is mass in kilograms, and T is temperature in kelvins
for our white dwarf, m is 1e30, T is 5e8K, so the heat energy stored is about 3.34e72 joules.
The energy lost my a white dwarf, radiated into space can be calculated by
F=oT^4 where F is flux, T is temperature in kelvins, and o is the stefan boltzmann constant.
according to HR-diagram, white dwarf is about 1e4 K
stefan boltzman constant: 5.6704×10^-8 watts per square meter kelvin to the fourth
F=5.67e8 W/m^2
Assuming 5e6m radius for white dwarf, 4pi*r^2=3.1416e14m^2
white dwarf outputs 1.78e23 watts, about 1/2000th solar luminosity.
the loss in energy causes the temperature to lower and emit less energy which causes the temperature to lower more slightly and so on.
the formula is
L(t)=8.03e-291/(2.68e-218+1.356e-250*t)^(4/3)
(that took an incredible amount of time to figure out)
where L is the luminosity in percentage of original luminosity, and t is the time.
the graph looks like this.
sooo uhh, about 10 million times longer than predicted by wikipedia. close enough.