Infrared (or IR) is the part of the electromagnetic spectrum consisting of wavelengths between 750 nm and 1 mm. It is commonly referred to as "heat", as temperatures produced by combustion, electrical discharge, or biochemical or other processes typically produce an infrared signature.
In 2151, Lieutenant Malcolm Reed had to refocus the infrared scanner on board Enterprise NX-01 in order to calibrate the ship's torpedo targeting system. The process took "the better part of a day." (ENT: "Fight or Flight")
Later that same year, the crew of the Enterprise discovered the rogue planet named Dakala but due to the heat generated from the planet's thermal vents, they had difficulty detecting anything using infrared scans. (ENT: "Rogue Planet")
A heat beam was a form of focused infrared energy that could be directed at a specific target. In 2267, the computer Landru used this type of technology to prevent the USS Enterprise from leaving the planet Beta III. (TOS: "The Return of the Archons")
Cadmium is a conduit for converting infrared light into electricity, emitting a charge when lit. In 2364, the crew of the USS Enterprise discovered Cadmium-based lifeforms which managed to destroy a laser drilling platform on the planet Velara III. (TNG: "Home Soil")
The VISOR device was capable of allowing its users to view both the infrared and ultraviolet light spectra. Lieutenant Geordi La Forge used this feature when boarding the Talarian freighter Batris to rescue three Klingons in late-2364. (TNG: "Heart of Glory") He also admitted to making use of it to view the backs of poker cards which would not normally be visible to him, but stated that he would only peek after the hand was over. (TNG: "Ethics")
In 2373, Lieutenant Tuvok detected the residual infrared signature of The Doctor's holographic program during an attempt to locate him and Kes, who had been kidnapped by The Doctor following a malfunction to his base program. (VOY: "Darkling")