$("td:contains('c')").html("new");

or, more precisely $("#table_headers td:contains('c')").html("new");

and maybe for reuse you could create a function to call

function ReplaceCellContent(find, replace)
{
    $("#table_headers td:contains('" + find + "')").html(replace);
}

Using eq() you can target the third cell in the table:

$('#table_header td').eq(2).html('new content');

If you wanted to target every third cell in each row, use the nth-child-selector:

$('#table_header td:nth-child(3)').html('new content');

You can use CSS selectors.

Depending on how you get that td, you can either give it an id:

<td id='cell'>c</td>

and then use:

$("#cell").text("text");

Or traverse to the third cell of the first row of table_header, etc.