This. A theoretically ideal “blackbody” emits electromagnetic waves/photons over distribution of wavelengths and intensities that vary as a function of its temperature. See this page, and take a look at the first plot you see. At low temperatures, a blackbody emits little total power (per unit area), and the peak of its emission spectrum is in the infrared range; the net result is that it doesn’t emit enough light in the visible range for you to see it. As a blackbody warms up, the total emitted power per unit area increases, and the peak of its emission spectrum moves to shorter and shorter wavelengths; at some point, you see a dim red glow, and if you warm it up further, you see it emitting a bright bluish-white light. Note that if a blackbody is hot enough to appear white or bluish-white, it’s also emitting a good deal of ultraviolet radiation, which means it’s harmful for your skin and eyes.
Note from that plot that for a blackbody at 5000K, the peak of the emission spectrum is pretty much in the center of the visible spectrum. This is nearly the temperature of the surface of the sun, and a 5500K blackbody has a spectrum that pretty closely matches the solar spectrum (before the atmosphere filters it). This brings up color temperature, which is an indication of the general color of a light source; A light bulb/LED with a color temperature of X appears (to your eye) to have a color similar to a blackbody at that temperature (though unlike a true blackbody, commercial available light bulbs don’t emit significant amounts of UV radiation). A light source with a color temperature of 5500K would be expected to appear the same color as the sun.
Note that you can measure the temperature of surfaces remotely using a pyrometer, which makes use of blackbody behavior. Cheap pyrometers simply measure the intensity of infrared light coming off of a surface at a particular wavelength; they have limited accuracy due to their built-in assumption of a particular degree of blackbody emissive behavior on the part of the target (as noted upthread, many materials and surface finishes deviate significantly from the ideal blackbody), but they’re awfully handy for measuring really hot things, things you can’t reach, and things you don’t want to touch, and they give you an instant result. If you’ve got a little more money, you can get a two-color pyrometer, which measures the relative intensities of IR light at two different emitted wavelengths, and calculates a temperature based on the ratio of those intensities.
For general heat transfer calculations (in a bulk power sense), the radiative flux of a hot surface scales with the fourth power of absolute temperature: an object emits X watts per square meter at room temperature (293K), and if you warm it up to 586K, it will emit 16X watts per square meter.
Steady-state temperatures and net heat fluxes for two interacting radiative surfaces can be calculated via the use of view factors, which help describe what fraction of an emitting surface’s power output is absorbed by a nearby absorbing surface; this varies depending on the shape, size, and distance of the two objects. If you flip to the back of any heat transfer textbook, you usually find an appendix containing instructions for how to calculate view factors for various configurations of interacting surfaces.