Hello,
Every body emits radiation, only because of the fact of having temperature (even at T=0 there is a residual radiation due to the zero point energy).
That is called "black body" radiation, and the frequency of the maximum emitted intensity is proportional (not directly) to the temperature of the body, and it´s independent of the body´s nature. At 25ºC matter emits radiation in far infrared-MW zone of the spectrum. Visible radiation is emitted at 900-1000 ºC (in fire, for example).
Yes, a normal body at 25ºC would emit radiation in far IR even in darkness, external natural light is not needed. But don´t forget that this is an energy emission, the body looses energy. If that body was in vacuum and completely isolated from external light it would loose energy decreasing temperature. In normal conditions a body mantains the temperature because it´s not in vacuum (heat conduction) and because it absorbs external light, so in that sense we can think that natural light enhaces IR emission, but it´s just an energy balance. The absorption of visible ligth increases temperature but it´s a different process.
If your question is: Would a visible ligth lamp at 1000ºC emit also IR radiation?
Yes, and the more powerful is the lamp, the greater is the IR intensity, but the MAXIMUM of the emitted intensity is not in IR, but in visible frequencies.