I use a little window screen on my intake side, makes it easier to clean. Some have tried dryer sheets, but those can overheat as well.
The intake was a lot more gunked up then I expected. Enough that I could scrap it off with my fingers. I cleaned it at the start of winter, definitely wasn't expecting that much already. My first thought was why is there is no screen. Might have to try adding one like you suggested.