I think something like this is what you're after (I created some data for this example):
data = Range@20;
tbl = Transpose[{data, data^3, data/25}];
ListLinePlot[tbl[[All, {1, 2}]],
ColorFunction -> Function[{x, y}, Darker[ColorData["Temperature"][tbl[[Round[x], 3]]], .2]],
ColorFunctionScaling -> False]

Setting the ColorFunctionScaling
to False
gets you the X
value which is then used to index back into your data to get the desired index of the color scheme. Note that if your actual X
values are not integers, you'll need to use other means (lookup, or an incrementing counter) to index into the desired color. Here's an example of that:
colors = tbl[[All, 3]]l
cnt = 1;
ListLinePlot[tbl[[All, {1, 2}]],
ColorFunction -> Function[{x, y}, Darker[ColorData["Temperature"][colors[[cnt++]]], .2]]]