I very much appreciate your update and I'm happy that the problem has been solved.
It is a frequent cause that one or more spaces or carriage returns are sent before the header section, because spaces and CRs are regarded 'harmless' chars.

Problem SOLVED.

Yes, you are right, the problem was on my template. After spending several hours trying to understand what was happening,
I removed some "Carriage Return" characters in a file from the template and the problem was solved. Nevertheless, that's weird because
we found "Carriage Return" characters all over the place in php and html files.
Anyway, thank you for your help...

I tested the module in a standard J2.5.16 install at position 6 (right column). I do not see the problem. Then I added <meta http-equiv="Cache-control" content="private"> to the template and still don't see the problem. So I am not convinced that the problem is in the GlobeWeather module.

The Globeweather version is the freeware one. I am using it on Joomla 2.5.16 version, and I know that this has to do with information that has been sent before the header information from Globeweather module. This happens when you send the "cache-control : private" message to the header...

Which edition of Globeweather is it (freeware, premium, business) and which Joomla! platform (J2.5 or 3.x) ?
Such error may happen if your website is outputting text to the browser before headers are sent, whereas headers should always come first. Even if only a space is printed before the header, this will give the problem. If you tell me what the URL of the website is (webdesign(AT)innato.nl) I will have a look.

After install and configure Globeweather, I get a warning on the module:
"Warning: Cannot modify header information - headers already sent by"

Why is this happening?