Vim visual selection and regexp

I am having a problem with the visual selection and running a regular expression replace. When I select some text that does not contain the whole row, and hit : to bring the command line up, and do something like

:s/T/t/

Then the first match on the line (whether it's selected or not) is changed. So, for example, I have the text

Test Text here

and I visually select the word Text, then run the above substitution, I end up with

test Text here

which is not what I want.

Any ideas how to achieve the right result?

Edit: The actual command line is

'<,'>s/T/t/

as defaulted by Vim when you press : with a visual selection.