Why exactly is infrared radiation called the heat signature?
Welcome to the PF.
When you do some searching on those two terms on google and on wikipedia.org, what kind of relationships do you find? If you add the search term "blackbody radiation", do you get more focused hits?
The energy of a photon in the infrared spectrum corresponds to many of the rovibrational transitions in abundant molecules, so it is very effective at being transferred to internal energy, or heat.
At temperatures normally held by many objects, the radiation is predominately in the infrared. So measuring the infrared emission is an indicator of temperature.
For very hot objects like stars, much of the radiation is in the visible, though there is still a lot of infrared emitted (of order 40% or so in the case of our sun, iirc).
Separate names with a comma.