The simplest way to solve this problem is with the introduction of Tableau 9.0, you can load .RData files directly into Tableau. Here is how you go about it:
1) Simply save() your correlation matrix as an .RData file.
2) Connect Tableau to the .RData file
3) Put "Measure Names" in the Columns field & "Rownames" in the Rows field.
4) Set Marks from "Automatic" to "Square"
5) Drag "Measure Values" over the "Color" Marks category
With the new R integration, this is very much simpler than any solution.