I received an email from one of my professors today and I am not sure if I should respond or not. The email contained the grade I received on a paper as well as my grade going into the final. I am not sure if I should reply with a simple "Thanks" or if I should just let it be. Also, the email was sent about 6 hours ago if that matters.
Summarizing all my comments as an answer,
I am not sure if I should reply with a simple "Thanks" or if I should just let it be.
It depends on the number of students the professor wrote to. If it is an invidualized e-mail for a limited amount of people (apparently your case), yes, a little "thank you" is the nice and polite way to go. (On the other hand, if the class is a huge auditorium of a hundred people, the professor probably doesn't want this amount of e-mails arriving in his/her inbox).
Also, the email was sent about 6 hours ago if that matters
6 hours, 24, 48, it doesn't matter. E-mail is not the same as instant messaging, and it is generally okay to skip a few days - especially in your situation: the professor is not waiting for your answer, it's just a nice thing to do, but if you wait three days or don't write at all, noone will notice.
Just write "Hi Professor X, thank you for taking the time to notify me!" and that's it!
If you are just stuck between a response and saying nothing, I would always go with a response to confirm the receipt of the email. But in your case, 1) it was more of an informative email and if you don't have any question or complaint about, you can let it go and 2) already 6 hours has passed. So, just let is be!
There's no correct response here, as it depends on the social mores of your group. Some people want to hear acknowledgement and will wonder if they don't get it, some people view courtesy emails like "thanks!" and "you're welcome!" as spam and will get upset if they do get it, and many more don't care either way.
My advice to you – ask your advisor sometime when there's nothing else important going on which one he prefers and just do that.