I was looking for a summer internship at a university as an undergraduate student. A few days ago I received an email from a professor expressing his interest in having me into his group. I replied. But now it's been nearly a week and I haven't received any responce. I am not sure of the reason. Maybe the professor is simply too busy. I understand that but I really need to schedule my summer plans now. How should I write an appropriate reminder email?
While the comment of Solar Mike is correct (patience), and you don't want to be a pest, there is one thing you can do that would be useful in any case.
Send a mail asking for any help on getting an early start. Are there papers you should read, for example? That keeps you in the mind of the professor, advances your cause, but also gives you something to do that can increase your knowledge.
But "nearly a week" is a nano-second in academic time.