My bedroom is hot in the summer and cold in the winter. Plus I have the thermostat control unit in my room.....so you can imagine my bills. What can I do?

Find a trustworthy heating and air conditioning contractor and have him balance your system, and consider moving the thermostat.

I forgot to mention that my bedroom is over the garage...I'm thinking that there might not be adequate insulation. How do I check other than cutting the walls?

As far as the room not being warm or cool enough. Any time a thermostat in in a room and the person is complaining that its not warm or cool enough that is only possible if the heating or cooling system is not properly sized and never shuts off. The room HAS to reach what ever the room stat is set at.Your issues are not the heating or cooling system.Its the insulation.

Its not the walls that is causing your discomfort during the winter. Its the floor. What has happened is what little insulation that is present below you feet has settled and a gap has been created between the top of the insulation and below surface of the floor. This allows for drafts to be created thus sucking out the heat. You either need to blow insulation into this cavity or remove the sheetrock and re-insulate with the proper thickness of the pink stuff that will plug the bays between the joists completly. Its very important to pack the insulation along the edges to prevent any additional drafts from starting thus sucking out more heat. Be sure to replace the sheetrock if removed with the correct thickness for fire safety. 1/2 inch is not correct.

As far as the cooling side. While the floor is critical for the heat, the ceiling is critical for the cooling. Check to see that you have at least 9" of the stuff in the ceiling. More in hotter or colder areas of the country. But that is a minimum amount with today standards. Also be sure to check that the soffit areas remain properly vented and that the attic itself is properly vented as well. This will help bring down the cooling load into the rooms thus the cooling bills.

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I forgot to mention that my bedroom is over the garage

Yes, that makes a bit of a difference. Home Care Club has the right idea, in that case.