Good question! Yes, you can think of heat in ordinary matter as nothing more than the jiggling of the molecules that make it up. To answer your question, first let me quickly explain what infrared light is. You probably know of something called electric fields; if your hair has ever stood up because of static electricity, that's electric fields at work. I'm also sure that you know of magnetic fields; these are how magnetic communicate a force. Together, the electric and magnetic fields make up something called the electromagnetic field.
Now, it turns out that when an electric field changes in time, it creates a magnetic field, and when a magnetic field changes in time, it creates an electric field. So, what happens when I "tweak" the electromagnetic field a little bit? Well, the changing electric field creates a changing magnetic field, which creates a changing electric field, which creates a changing magnetic field... you can see that you get a runaway process, where the changing electric and magnetic fields continue to create each other and keep each other going. This creates what's called an electromagnetic wave: a wave of oscillating magnetic and electric fields that spreads out from whenever you created the first disturbance. It turns out that this wave moves at precisely the speed of light; that's because it is light! Light isn't the only type of electromagnetic wave, though; depending on the frequency (that is, how quickly the wave "wiggles"), you can get radio waves (which wiggle the slowest), microwaves (that's what microwave ovens use!), infrared light, visible light, ultraviolet light, X-rays, and gamma rays (which wiggle the fastest). Together, all of this radiation makes up what's called the electromagnetic spectrum.
Now, where does this figure into your question? Well, remember that molecules are made up of atoms, which are made up of electrically charged particles called electrons (there are also protons and neutrons, but the electrons are the most important part of the explanation). When the molecules wiggle because of heat in an object, the electrons wiggle, too. But wait! Electrons are electrically charged, so they create an electric field; if I wiggle an electron, I wiggle the electric field, too, and that's exactly how I create an electromagnetic wave! So heat gives off infrared light because the wiggling of the electrons in an object makes them give off infrared electromagnetic radiation. Infrared cameras don't really see the wiggling of the molecules; they just see the electromagnetic waves that the wiggling creates.
As you can guess, the molecules in a hotter object wiggle faster. So, something at room temperature, or slightly warmer (like a human body), only gives off infrared radiation. But as you make something hotter, the electrons wiggle faster, and they create electromagnetic radiation of higher frequency, which becomes the visible light we see. That's why as something gets really hot (like coals in a fire), it starts to glow red, and if it gets REALLY hot (like, say, the surface of the sun), it glows white.
I hope that explanation helped!
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