Given a high enough temperature, or a high enough electrical field, can we make every material emit visible light?
"emit visible light" Selection rules! First Law. A clean, pure, transparent and colorless monocrystal diamond has a Debye temperature around 2230 K. Heating diamond to 1000 C (1273 K) does not render it luminous in the visible. Diamond optical absorption edge vs. photon energy at different temperatures, and with various impurities ((1) is intrinsic),
(Isotopically pure C-12 diamond will be more extreme. Diamond is kinetically labile to graphite beginning around 1000 C in air. Under inert gas or a mildly reducing atomsphere, it lasts until about 1500 C.)
Yes. Every object whose temperature is not 0 K radiates. That means that every object glows in a sense. For everyday objects at everyday temperatures, the wavelength of the glow is around $10\, \mu m$, far in the infrared, and far outside the range of human vision. As you heat the object, the wavelength of the radiation gets closer and closer to the visible range. Any object will eventually get hot enough that the glow will become visible, if it hasn't burst into flames first.
Electric field will not cause an object to "glow", but in a strong enough electric field electrons will be pulled from the object, and light will be emitted by various mechanisms, some not directly connected to the object. In gases, the light can be continuous and might be described a a "glow". Most of the time, though, I think I would call the light emitted in an electric field as a "spark", but there are a lot of different situations, and the light will be different in each situation.