I want cooler supply air in the bedroom than in the living room. Is this possible?

Yes, it is technically possible to achieve cooler supply air in the bedroom than in the living room by installing a cooling coil on the supply air ducts. However, this is often a costly solution. In most cases, it is more cost-effective to invest in other measures, such as external solar shading, improved window shading, or reducing heat gains in the room. Cooling via the ventilation system should generally be considered a supplement to such measures, rather than a primary solution for room cooling.