A high power incandescent light source can certainly ignite paper, wood etc, and this has been demonstarted both to prove a point, and in a number of accidental fires.
Incandescent sources, and some types of HID produce considerable infra-red, and it is mainly this that ignites materials, the contribution from the visable rays being limited.
In the case of a source that produces very little infra-red, such as LEDs, then the visible light, could ignite materials, but in practice it is unlikely except in extreme cases.
The visible light is not hot in itself, but when absorbed by a non-reflective surface, is turned into heat which increases the temperature of that surface. A perfectly reflective surface would not become heated, and an imperfectly reflecting surface would be heated to a much smaller extent.
Lasers can readily ignite materials because the energy is concentrated in such a small area.
Other (visible only, no IR) light sources cant normally concentrate enough energy in a small enough space to start a fire, though it is no doubt possible.