If I have someone write a letter of recommendation for me, should I send them a thank you note?

A simple thank you, privately, is fine. But if you actually get the job, you should certainly write a note, and depending how well you know him, send a nice potted plant or something. Better not alcohol in this situation, though again it all depends.

Without hesitation.

A simple thank you, privately, is fine. But if you actually get the job, you should certainly write a note, and depending how well you know him, send a nice potted plant or something. Better not alcohol in this situation, though again it all depends.

I would say most certainly especially if the position or college you want to be considered for approves you. It is a way of saying more than thank you. It says you are appreciative and you have home training and not just a consumer.

Without hesitation.

I'd probably keep it to a simple verbal "thank you" but pick your moment i.e. make a point of talking to him after class and don't mix it up with another reason to see him. So it is clear that you specifically made the effort to talk to him to say thank you, nothing else.

I think a Thank You note would be very appropriate. However, I also think that a gift would be a bit too much.

a bottle of fine wine would be appropriate

A thank you note is good manners,a gift is optional depending on how much you appreciate it. In the case of a professor,something tasteful and of good quality,but not too personal or expensive. Maybe a bottle of 12-year-old Scotch,if he likes alcohol.