Does a light bulb that produces more light also produce more heat?
Yes. When comparing light bulbs of the same type, a bulb that produces more light (or is brighter), produces more heat also. This is largely due to the fact that bulbs are not capable of converting all the input electric energy into visible light. As the efficiency with which light bulbs can produce visible light is less than 100%, with an increase in the production of visible light the production of infrared radiation or heat also goes up.
In most types of light bulbs, the ratio of energy dissipated as visible light to the energy dissipated as heat increases as the wattage increases. The same amount of light produced by two smaller bulbs will lead to the production of a larger amount of heat than if the visible light were produced by a single large bulb.