By "apply this process", you mean to put the soil or water directly in the furnace? The fungi are performing chemical concentration/separation. Depending on how hot you needed to heat the soil to get meaningful separation, you might end up damaging other properties of the soil by heating it so hot.

With water, it would have to be super contaminated for the majority of the dissolved compounds in the water to be heavy metal compounds, so distilling the water would still leave you with some mixture that you'd probably want to chemically separate. At least you wouldn't be causing any damage to the water by boiling it away, but it would be pretty energy-intensive.