My laptop is getting to the point were it overheats and shuts down if uses 100% CPU for about 15 seconds. If I don’t have an adapter, my processor speed is cut in half and I don’t have to worry about it overheating anymore. Is there a way I can lower my maximum processor speed without unplugging the adapter?

Yes, the power settings allow you to adjust all of the performance characteristics based on whether you're plugged in or not. Check in the control panel for power options.

The only thing my power options allow for me to do is set when my computer hibernates or goes into standby.

If this is a new thing, you might also want to check that your fan ducts aren't clogged.

Sounds like you might have to enable advanced power management.

See if this helps.

Dealing with Windows's Advanced Power Management (APM)

I had a similar problem with my laptop (not shutting down, but temperatures over 95C).

I took apart my laptop and cleaned a thick layer of dust off of the heatsinks; almost no air was flowing. When I turned my computer on again, the temperature under load was about 40C cooler.

Your computer won't just mysteriously run hotter as it ages; there's likely a problem with the cooling system, and if it's just dust clogging the heatsink/fan, it's easy to fix.

forget about APM (well use it but)
all thats gonna do is hide the problem, as has been suggested you prolly need to clean the machine

You should definitely check out Notebook hardware Control .. it has the ability to Lower CPU and GPU Levels. This is also what I use on my laptop to get extended battery life + to lower heat when I'm not playing games.

You will not be disappointed. I've been using this for 2 years and still use it to date.

But as others suggest, you should clean out the dust. Use a compressed air can, these bottles of magic helped me in many ways.. and not just computer related stuff either ;)