This will be determined by a few factors. First, what is the resolution
of the system? The pixels in a given angular field will be a constraint.
Second, what sort of sensitivity does the system have to the temperature
difference? Liquid nitrogen cooling can extremely enhance the sensitivity
of your detector, and it also helps if the background temperature is low to
Third, what is the noise floor of your system? By that I mean, "what
sort of image noise is present in the image sensor?" You see, image noise
can blot out the heat signature, and in most systems this is helped greatly
by cooling (see note above about liquid nitrogen). But even in cooled
systems, there is random atomic noise or thermal noise that is generated
inside the image sensor, inside the amplifiers, inside every component in
the signal path and processing path. Even impedance mismatches can
contribute echoes and signal reflections that can add to the noise floor.
Fourth, what is the f-stop of your system? Anyone who is familiar with
cameras and optical systems is familiar with the effect that your aperture
versus its focal length can have on many aspects of image quality. "Speed"
is the attribute usually associated with "f-stop", by the simple logic that
the larger your input lens, the greater light it can gather, and that
greater the magnification, the less effective the available light is in
creating an image.
In other words, a large primary lens or light collector and a short
focal length can give you some very good image gain. On the other hand, you
can lose a lot of your image as unfocused light if you use too large an
f-stop, trying to compensate for low light (or thermal) levels.
There are other factors, and I am sure to have forgotten some important
ones, but to be brief, you need a large input lens, short focal length,
higher resolution sensor, a cooled or thermally stable system, and a lower
outdoors ambient temperature- then, it is possible to detect body heat to
distances of kilometers.
Experiment and see how these factors add up.