To get a star's true color one needs to use spectroscopic equipment. Estimating temperatures by visual colors seen through a telescope, however, is inexact at best. Many factors influence what we perceive the color of a star to be. The most important factor is that each persons eyes are different and see shades of colors differently. Also the color of one star may affect what we see as the color of the double.
Many people can disagree on the color of any given star.
So be satisfied in knowing that a star that appears to you to be closer to the red end of the spectrum is cooler that one that appears closer to the blue end. The important thing is to enjoy the colorful spectacle. It is easy to find lists of good doubles stars to observe. Just about any good astronomy book will have such a list. Alpha Canis Maj.