Arduino Mega 2560

Hello! I got a normal Arduino Mega 2560, I think R3 here. It has no ethernet shield.
Now my question is: Is there any possibility to use the pins like one or something?

I'm currently gathering Temperature from a sensor and would like to push it over the network. An idea is that my webserver would catch the value and represent it on a website.

Is this project just not made for this Arduino model or is there a way to do it? Are there extensions?

Best regards,
XaTrIxX

This one won't work for you?

Is it like an ADDON for the arduino or is it a complete Arduino? I'm not understanding it yet. It looks like a separate Arduino?

It is a board that plugs onto the female headers of the Arduino.

Oh I see. Thanks!