I found a 1500 Watt blow dryer, positioned it 1/4" above a scrap tile piece, turned it on high for five minutes with zero negative effect on the tile.
No blistering, no discoloration, nothing. This even suprised me.
I then put a puddle of petroleum based Goo-Gone on the surface for several minutes, thinking it would soften the vinyl. But again, no ill effects.
So far, the tile looks viable, especially since the total cost of materials to do the counter top was $12.00.
Yes, the really best way would be with real tile or cultured stone tile. And the cost would not be too bad. But the installation would take special cutting equipment and grouting technique.
I did this job with left over tile from the floor project and left over silicone from the shower project. It didn't cost me one cent additional to do it.