If the MP3 is streamed you, would have to record It using the sound card setting "Record what you hear" or "Stereo Ouput" (depending on what the manufactorer of your soundcard calls it ). Unless... you could find the actual MP3 audio file, where you could just download it. The reference to a streamed mp3 is a .m3u file which does not contain the audio. . However you could try re-retyping the URL in your browser with an .mp3 extention instead of the .m3u.... and if you feel lucky, well do ya punk?, the web master may have put the mp3 audio file in the same folder as the .m3u reference file, and then you could download it directly by right-clicking and select "Save target as".

And yes, if recording the stream, it would record as a wave... but you could just save it as an MP3. The actual wave file would only be temporary. If you plan to edit, process or do anything else afterwards, save as a wave, since every time an MP3 is rendered, it is re-compressed and quality is degraded each time.