Hot or cold rooms is always a distribution problem and not an equipment problem. The Industry standard for room to room temperature variation is +/- 3 degrees Fahrenheit from the thermostat. If your home is energy star certified it had to be inspected by an independent company for room to room air flow as well as other criteria.
There are many factors that control room temperature. Heat gain / loss varies through out the day. Closed supply vents and doors significantly affect air flow and system capacity. Insulation, design or construction errors frequently cause major air flow problems.
Think of your HVAC system as being able to supply a limited number of buckets of air. If your total HAVC system capacity is 10 buckets of air and you want to add 2 buckets of air to a room those 2 buckets will be subtracted from one or more rooms in your home. Arbitrarily changing air flow to to one room can just relocate the problem to a different room.
The proper way to address this problem is to have your HVAC company do a room by room heat load calculation then an air flow survey and static pressure test. Once a base line is established a duct design can be made and compared to the actual system. Then adjustments can be made. This is an iterative process in that each time an adjustment is made the air flow survey has to be redone to confirm results. Air takes the path of least resistance and that path can change with each adjustment.
Things to consider:
- The initial investigation for a single system home will cost hundreds of dollars. Additional systems and or floors add to the complexity and cost.
- The degree of control over room to room temperature variation directly affects the cost of correction ranging from a hundreds to thousands of dollars.
I would be happy to answer any specific questions you have regarding the design, installation or operation of your HVAC system