That figure of 98% that you'll see on many dodgy websites was obviously copied from these sites by Plimer without quoting the source - because there is no source
It's urban legend.
The real figure taken globally is around about 50% percent, but there are other feedbacks apart from water.
Climate sensitivity for a doubling of CO2 is around 3 degrees C (plus or minus 1.5), of which about 1 degree is due to greenhouse gases including CO2, methane nitrous oxide etc, using the forcing equation, which in itself is basic physics:
dT=[alpha]ln([CO2]/[CO2}orig)/(4[sigma] T^3)
(edit - correction - that's the forcing equation for CO2 only. We generally use the same equation for other gases by expressing them in CO2 equivalents (CO2-e)
Another 1 degree C is due to water feedbacks, and all other feedbacks account for another 1 degree or so. Those 'other' feedbacks include albedo, clouds, lapse rate, arctic methane release and reducing CO2 uptake by the oceans as the pH falls.
Incidentally some denialist sites quote very low or even negative water feedbacks. It depends on exactly what they want to argue at the time. It's easier to win an argument when you don't have to stick to the facts.