In the episode Identity Crisis of Star Trek TNG, wouldn't Geordi have been able to see the heat signature of the "invisible" aliens?
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From the transcript
OGAWA: Sorry to disturb you, Doctor.
CRUSHER: That's all right. What's happened?
OGAWA: I thought you should see this. (Alyssa shines a torch on Susanna)
CRUSHER: Her skin is simulating light. A radiant reaction. Some sort of mimetic ability?
OGAWA: That's not all. Her body temperature is dropping.
CRUSHER: It's as if she's generating a disruptive field. I can barely get any readings off her now. What's her rate of transformation?
OGAWA: It's increasing.
The aliens were not only mimicking the visible light spectrum (causing most of the crew to be unable to see them), but were also matching their body temperatures to accomplish the same sort of mimicry in the infrared spectrum, and (since we know he can't see them) presumably in the other spectrums in which Geordi can see as well.
That would depend entirely on the process which was causing the aliens to be invisible. Geordi can't see everything, but he does have a much broader range of "vision" than normal humans do. If the process is similar in concept to a cloaking device, for example, the rays of energy that Geordi can see would be bent around the invisible person and Geordi would not see them. Or if it were similar to the camoflage technologies portrayed in some movies like GIJoe or James Bond, where an outer layer hides what's behind that layer by superimposing an image from the opposite side. Again, even Geordi's advanced vision could easily miss what was being hidden. Yet another option is if the hidden alien is hidden due to something taking them slightly out of phase (a trick used in other Star Trek episodes). There too he would likely miss what was there.
So there are quite a few ways for an alien to hide themselves from being seen, even to Geordi's advanced vision abilities.
The aliens emitted a electromagnetic field that redirected all wavelengths of light including the infrared and ultraviolet light that Geordi is able to see in using the VISOR. This redirection worked for their own personal radiations.
As usual, the Enterprise crew creates/modifies a technology to solve the problem:
The show had a technical error: