How to stay in connection with a professor when you want to apply for the position in his group in next quarter? I got a strong recommendation from my former supervisor. He wants to recommend me to one of his former colleagues who happens to have no position now. So I have to wait until the Spring Quarter. But I want to stay in contact with him because everything could happen during this period from now to next March. 

Basically, in that university, the professors have the absolute power. If I can get permission from him, I can secure this position. And I really value this opportunity as he is like among the top 5 in our field. 

How should I do? I have no idea what should be in the email which could increase my admission chance and would not bother him. I guess he must be busy every day.
You could contact him to ask for him to advise you on some papers for you to read that are related to the work for that position. This way you have a good excuse to contact him, you gain extra points for showing interest and getting prepared in advance, and also provides you with another excuse to contact him in the future to clarify questions you may have from reading those papers.