Okay, Heat detecting equipment basically just uses thermal imaging. In a word: Infrared.
So any true, at least functional, invisibility (besides just painting yourself green or being shaped like a Stealth Bomber) would either bend ala Einstein the light (visible and infrared) behind the user to be in front of it, or would imitate it. Either way, heat detecting equipment as we know it would not work.
Example of bending:
L=light
o=Me, (OK, oo because I am fat and take up two ASCII spaces in reallife)
|=stupid spam filter won't let me use long spaces, imagine it's empty space
||||||| ______
____/ ||oo ||||\_______
||||||\_______/
So, either computers and flexible monitors that work VERY FAST, or a portable gravity amplification/nullification device.