What are decribing is a very common procedure. You can buy a register which can be opened closed as needed. The installation should not be too difficult. The register would be attached with sheet metal screws.

The only drawback is you would be stealing some amount of air flow from the rest of the house. You may not want to do this if your current air flow is weak.

Thanks mike.
Do they sell registers that are specifically for the side of ducts?
Our house cools really nicely, so I think we could stand to give a little to the basement. We could always close the register off if it doesn't work out.
Thanks!

You can use a standard register. I am sure you have find them at Lowe's or Home Depot.

Have you checked the basement for radon?

Yes, we have a radon fan that takes care of under the small basement floor and a radon barrier in the crawl space. Why do you ask?

Bringing up air from a basement that has not been checked for radon is not a good idea. It sounds like you have that covered.

Is the basement dry or humid? If humid, it will add a more significant load than you might expect from the temperature.

What kind of water heater do you have there? Depending on your climate and what you use to heat water, you could consider adding a heat pump water heater.

I should have made more obvious that a HPWH will cool and dehumidify the basement, however, it will only do it when you are using hot water.

I am still thinking about this. What are the sources of heat down there aside from the water heater? If that is it, the HPWH might solve your problem if it does not make it too cool in the winter.