Eminem -- Grants Wish ... For Terminally Ill Fan

Eminem isn't always the angry rapper who rips people on tracks ... sometimes he's the sweetheart who visits the home of a terminally ill fan ... and doesn't tell a soul about it.

The fan in question is 17-year-old Gage Garmo ... who has been diagnosed with Osteosarcoma, a rare form of bone cancer, and has been told he only has one week to live. Just three days ago, Gage's friends and family started up the hashtag #GetGageGarmoToMeetEminem ... in an effort to ... well, it's obvious.

And it worked. We're told Em arranged for a home visit at Gage's place in Michigan ... which is only about 20 minutes from where Em lives.

We're told Em was adamant he did not want the visit to become a media spectacle -- and quietly arrived to Gage's home around 5PM Sunday.

The two spent around an hour together -- talking and hanging out. We're told the whole thing meant a lot to Gage, who was in good spirits during the visit and after.

The Real Slim Shady ... is just a big softy.