You know that that claim came from a book and was never peer reviewed? Anybody can write a book. 

The ice caps are thicker (regionally, although total ice mass is declining) because warmer air holds more moisture = more precipitation (as snowfall) - have you noticed it doesnt' snow when it's cold out, only when it's close to freezing?   This talking point confuses "warmer" with "warm".  Antarctica can get 20 degrees warmer and still be well below freezing - which means increased snowfall and thicker ice.