In the example, based on a white dwarf whose age is 1.701 billion years, the temperature is between 7000 (the 1.5 billion value) and 5500 (the 2.1 billion year level). The difference between those two numbers is 1500. The actual age is .201 billion beyond 1.5 (or 0.799 more than 2.5) since this is a billion year period, you can either multiple .201 x 1 and then multiply by 1.5 and subtract that number from the higher temperature - that's the -.201 x 1500 +7000 - it could also be 7000 - 0.201 x 1500 - same answer) or you can multiply .701 by 1 and add it to 5000. Also same answer of 6699.

Now I think you caught me at an edit gap here, (which sucks, because I just said the book was good to print) because I stopped there and did not do another step which I detail on page 227, which is to adjust the temperature for mass, and that would be - in the example - 0.49 /0.6 or 0.817 so the temperature in the example ought to be a final value of 5471. Hardly matters because the luminosity is so low as a potion of the binary, but that was missed.

In your example, the white dwarf is 0.455 billion years old, which is fairly close to 0.5, but to be precise, it is 0.5-0.455 or 0.045 short of 0.5. Since the two values on the table on page 227 are for 0.1 and 0.5 billion years, the difference between those ages is 0.4 billion, and the difference between the temperatures is 25000-10000 or 15000, so we can say that it is 0.045 billion / 0.4 billion = 0.1125 x 15000 (the difference in temperatures) = 1687.5 above the value at 10000, which is 11687.5 (yes, that's backwards from the example, it would also work by taking 25000 - 0.8875 x 15000 = 11687.5 { with 0.8875 being = 1 - 0.1125} ). So including the mass differential we have 11687.5 x 0.58 /0.6 = 11297.9 or ~11,300.

(And yeah, I tried to do this today with the iPhone calculator app, failed to get consistent results, and had to dig out Excel to use as a scratch pad to make sure it was right - coffee must be defective)