I work as a temp worker, from a temp agency, in a large corporation.
My contract is due to expire, and because of various employment
regulations, there is a chance that they will not extend it despite
the fact that I am a very good worker (if I ma say so myself), since
they could hire a temp for a limited period of time, that is about to
expire.

I would like either to receive a regular job in that organisation, or
that my contract will be extended.

I already spoke with my immidiate bosses, they are all sympthetic and
say that they'll do whatever they could, but I have no idea whether
they do something or not.

I know for sure that the organisation is short of personnel in some
departments (stuff that I could do) and is actually hiring new people
without experience, but (may) not extend my contract - someone with
experience!

Now, there's a "big boss" that always writes in his emails "my door is
always open" blah blah.

I am wondering if to approach him (write to him, I mean): 

- On the one hand, I have nothing to lose. If they don't extend, they
don't extend. Of course, it might show my commitment to the place and
get me the regular place in the company.

- On the other, it might be interpreted as bypassing my immidiate
bosses; or as rudness. I mean, we all know that "My door is always
open" doesn't really mean that.

What shall I do? I am seeking advice.

My advice would be to go talk to him, don't write (at least not as a
first step).  Not directly about your situation with the company, but
to express interest in the company's business model and prospects. 
Mr. "My door is always open" is probably not too different from the
rest of us and loves to talk about himself and his
contributions/accomplishments.

If you are a good listener, tap into that and you may accomplish two
things.  The first is to get a better idea about where the
opportunities opening up in the firm are likely to be.  It's always
better to have information than to guess.

Second, you're apt to make your name recognizable to the big boss, and
this could make all the difference in whether you get extended,
regardless of whether the subject comes up in conversation.  No need
to tout yourself, you'll make a better impression by asking
intelligent questions about the business.  A top executive running a
successful business will almost always respect the initiative of a
"self-starter".

If in the course of events you do find out that a suitable opportunity
has opened in a lateral position or even one better than you now have,
an email or other written communication asking to be considered for
that position will at least have some context for the decision maker.

To prepare for this "cold call" meeting, do your homework.  Of course
you've learned a great deal about the corporate culture and so forth
by working there, but many employees at firms have no grasp on the
financial parameters of their company.  Do them one better by
searching Google, etc. for trade information (or, plug-plug, by
posting a specific question on Google Answers).

best wishes, mathtalk-ga

It might not be a bad idea to have your resume (updated of course) and
a cover letter prepared (and maybe with you) should you get an
audience with Mr. "My door is always open."

I'll also second mathtalk-ga's suggestion--do your homework on the
company ahead of time. That always seems to impress them.

Good luck!
luciaphile-ga

Piripiri:

Great advice from my colleagues above and be certain before talking to
your boss that you will not be in violation of any rules of the temp
agency.  By definition, you are an employee of the temp agency.

Best regards,
journalist-ga

One thing to keep in mind:
You are currently employed by the temp agency, not the company you
actually "work for."  If you make a deal directly with the company,
this will cut out the temp agency, and they will probably be unhappy. 
In fact, the contract you signed with the temp agency may include a
clause preventing you from taking this action.  (Whether such a clause
is actually enforcable depends on what state you are in.)  At a
minimum, if you go "behind the back" of the temp agency, you should
not expect to work for them ever again.  Which maybe is fine with you,
just be aware of the possible consequences.