First off...can you upload some sample photos somewhere so we can see the effect?
Owning a 7D myself, and having done some long-exposure star trails shots about a year ago when I first got it, I can at least state that I have not encountered the same issue. At least, not at ISO 100. On longer exposures, if I expose for minutes rather than just seconds, obviously FPN, or fixed pattern noise, begins to exhibit. Every digital camera has FPN as they are the result of tiny physical defects that affect charge buildup and reset for the affected pixels. They are usually called hot pixels, and as exposure time increases beyond a certain threshold, they become increasingly apparent. Most RAW editing software can easily identify and eliminate hot pixels, either automatically with the demosaicing algorithm, or via the NR tools.
If you are really seeing excessive noise at ISO 100 after 30 second long exposures, or if the hot pixels are particularly bad, it sounds like you may have a bad sensor or something. Noise will usually increase as sensor temperature increases, but not so much at ISO 100 that you couldn't see the image at all. Enabling long exposure noise reduction in the camera will double the exposure time, but it can automatically remove readout and FPN from the image as it saves it to the CF card. If you shoot a 30 second exposure, after the shutter closes the camera will expose a dark frame for another 30 seconds with the same exposure settings, read out a bias frame sensor at 1/8000th ISO 100, and combine all three images to remove bias and sensor noise in the final image.