In the context of a Hertzsprung-Russell (H-R) diagram, which plots stellar luminosity against surface temperature (or color), a cooler but very bright star would be found in the upper right portion of the diagram. This region is typically occupied by red giants and supergiants.
These stars have relatively low surface temperatures (hence they appear red or orange), but they have enormous luminosities due to their large radii. The cool temperatures are combined with high luminosity because while they may not be very hot, their vast sizes enable them to emit a great amount of energy.
So, if you are adjusting the luminosity while keeping the temperature in a cooler range (around the middle), you would ideally place these very bright, cool stars in the upper left quadrant of the H-R diagram.