There are a few camcorders out there that have an infrared facility, but it's never perfect. Leaving the detector open to infrared all the time causes blurring of the image because the IR image overlays the visible image and it's out of focus.
I came across a site describing how to convert a digital camcorder to run as a purely infrared-sensitive camera. You need an IR filter for the lens, and you have to remove the blue-green filter in the camera optics, which means you need to disassemble the camera.
This is not a trivial modification. There is a better than average chance of starting with a working camera and ending up with a pile of worthless junk.
If you get it right, the camcorder becomes a pure-infrared device, that is, it only reacts to infrared light. Note that changing it back to a visible-light camera involves taking it all to bits again. It's a permanent modification so don't do it to your only camera!
The author of this modification describes using the camera in daylight, but it should also work at night with IR illumination or perhaps without the IR filter over the lens.
I intend to try, as soon as I can locate a cheap, but working, second-hand camera.