Is it reasonable to start a PhD during the Master's dissertation semester? I would like to start my doctorate in the same university during the last semester of my Master's. Do you think it is wise to do this?

Think that I will have to start writing my Master's dissertation, meanwhile taking PhD courses (both starting 2016's fall and finishing by mid 2017's spring) and right next to start my PhD thesis (2017's fall).

So, what is your advice?
I think it's an extremely attractive proposition, but not necessarily realistic. For a start, your master's degree/dissertation result most likely won't have come in by the time the PhD term starts (and your master's dissertation will give your institution a good idea of what your PhD performance will be). For my own institution, I submitted my dissertation mid Sept and my mark came in early December. There's no way I could have started a PhD a week after submitting my dissertation! But your deadlines may well be different. 

Secondly, how you would have time to do a well-thought out PhD proposal while you are doing your master's dissertation is beyond me. Don't do too many things at once. Bear in mind that when your master's dissertation finishes it's a good idea to start thinking about your PhD topic pretty soon afterwards anyway. Work through the proposal carefully and thoughtfully during the Autumn and submit before Xmas/Jan - especially if you are going for funding. Then you will have to work on your supporting statement.

Thirdly, it may be a good idea to collect yourself and have a year between master's and PhD. I'm currently at that point and while I do miss academic responsibilities, I do have a couple of things to involve myself with in my field. Join your library, do some reading. You may also appreciate a year [well, it's less than a year] to have a little time out before your full-on PhD.

Summary: while it's extremely attractive as an idea to do PhD straight after master's I don't think it's practical. You need mental and physical space to do things well and to commit to both properly. Don't push yourself too hard and don't be scared of your year in between the two. As you must know from your time in master's, it's better to pace yourself rather than to rush things.