It can be done easily in Awk:
$ awk 'NR==FNR {a[$1] = FNR==1 ? $2 : sprintf("%.2f",$2); next} {print $0,a[$1]}' File2 File1
hc Value mean
cluster0 0.1 0.35
cluster0 0.2 0.35
cluster0 0.3 0.35
cluster1 0.3 0.40
cluster1 0.5 0.40
cluster0 0.8 0.35
cluster2 0.9 0.90
cluster2 0.9 0.90
cluster0 0.0 0.35
The steps are:
* for lines in the first named file (`NR==FNR`), create an associative array (or hash) indexed by the first column values and containing the second column (mean) values. If you don't need the mean values to be displayed in floating-point format, you can simplify this step to `NR==FNR {a[$1] = $2}` which treats all the values (including the header) as strings.
* otherwise, print the line followed by the value in the array whose index matches the first column