Not if you're using incandescence (LEDs and fluorescence use different mechanisms where this tradeoff doesn't exist in the same way). Incandescence is black-bod

Not if you're using incandescence (LEDs and fluorescence use different mechanisms where this tradeoff doesn't exist in the same way). Incandescence is black-body radiation and the thing about black-body radiation is that as the temperature increases both the total energy given off and the proportion of higher energy radiation (useful visible light) to lower energy radiation (waste infrared) increase. So a hotter incandescent lightblub is more efficient than a cooler one (at least up until the point that it's so hot it starts giving off too much ultraviolet light, but that corresponds to a temperature at which no material is solid), though still pretty shockingly inefficient. Note that heat output and temperature can change seperately: a bulb running at a higher temperature (what I mean by hotter) can either have more light output for the same heat output, or less heat output for the same light output (for example, if the filament is shorter).