Been there, done that, on a fir floor. Used a scraper and a hell of a lot of effort to get it up, then sanded and painted the floor. After doing that, I purchased a pneumatic scraper from Harbor Freight because I never wanted to face that problem with a hand scraper again.
I didn't try heat. A 20 grit belt sander might take care of the problem but it would take a lot of paper since it clogs up pretty fast.
In retrospect, I might have been further ahead to simply put down a new wood floor right on top of the lino. If I had had access to Lumber Liquidators at the time and was able to find a small lot of discontinued wood flooring at a good price, it would have been an easier choice.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13