keyboard Overheating

You didn't give your laptop model number, so I don't know if you bought new or used. If it's new, then internal dust shouldn't be an issue. Regarding ventilation, usually the intake vent is on laptop bottom, while the exhaust vent is on the left side.

Heat and ventilation are issues with pretty well all modern thin laptops. You might want to do what I did:

I took a strip of lumber, about 3.5 cm. wide x 2 cm. high (1.5" x 3/4"}, and the length equal to the width of my laptop. I routed out two notches to accommodate the laptop's rear feet. The rear of the laptop sits in those notches, propping up the rear by 2 cm. That provides better ventilation underneath the laptop and makes it easier for the fan to draw in air via the bottom vent. 

I bought a new Dell laptop core i7 a little over a week ago, but I only started using it for work the last two days. My keyboard was running very hot after two 1/2 hours. I'm just running Word and Dragon Naturally Speaking. I don't know how to check if other things that I'm unaware of are running in the background. My old Dell, approximately 7 years old, ran Word and Dragon without this headache.

I already have the back legs of the computer raised; no vents are blocked, but the fan runs a lot, especially when the keys are hot.

I'm concerned if I use the Dell optimizer and put it on "cool," the performance will slow down too much. I was told this core i7 would handle Word and Dragon with no problems, so how do I cool the computer down without losing performance?