Yes, using a heat dryer, be it electric or gas powered, will wear out your articles of clothing much faster.
It's a pain in the ass, but I hang dry a lot of my clothing now; the exceptions being socks, underwear, gym clothes, and old stuff.
As an example: I have uniforms for work (I'm a firefighter/paramedic, we wear dark blue station uniforms) that look as dark and crisp as the day I was issued them---and this is 2 years later.
The ones I used to heat dry were well-faded and worn in less than a year.