There was a song in the 80s with lyrics something like:
"In the cool, cool, cool of the morning...." It was a
hard rock song. I need to know what that song is and
a souce to get the mp3.

Great song. The title is "Stayed Awake All Night," originally recorded
in 1972 by Bachman-Turner Overdrive, and later covered by Krokus.

"In the cool cool cool of the morning 
That's when Im coming home
In the cool cool cool of the morning 
That's when I'm coming home

Stayed awake all night
Stayed awake all night
Stayed awake all night night long..."

Complete lyrics are available here:

Upseros.com: Lyrics
http://www.upseros.net/contenidos/lmusicales.php?c=4156

(This is a Spanish site, but the lyrics, as originally written, are in
English.)

You can listen to a clip of the BTO version of the song, and buy the
CD at a bargain price, here:

Cheap-CDs.com/Bachman-Turner Overdrive
http://cheap-cds.com/surf/disps/58934

The Krokus cover (which is probably the version you remember, since it
was a big hit in the '80s) is available on CD here:

ArtistDirect.com: Krokus Headhunter
http://www.artistdirect.com/store/artist/album/0,,116579,00.html

Regarding availability of an mp3, both the BTO version and the Krokus
version of "Stayed Awake All Night" are currently listed on Kazaa.

My search strategy: 

I remembered this song from the early years of MTV. To find the
lyrics, and CDs which contain the song, I searched on Google using the
keywords "stayed awake all night." To verify that an mp3 was
available, I logged onto Kazaa and did a title search for "stayed
awake all night," which turned up sources for both the Krokus version
and the BTO version of the song.

If anything in my answer is unclear, or if any of the links do not
function, please do not hesitate to request clarification.

Best regards,
pinkfreud

Perfect