It's not a matter of "temptation", really - though the Shadow tempted Rand to save Min's life, and it worked.... and threatened to end Shai'tan his victory.. until it actually made Rand hit the bottom of the barrel, and he can out of there transformed completely.

What the Shadow mostly managed to do is to twist Rand's perspective on his role (he approached this through the perspective of an Emperor and warrior rather than a religious/inspirational figure) and what the Last Battle is really about, a choice between the Pattern or its end. A lot of the Shadow's efforts (though its agents where not often conscious of what they were doing) were meant to encourage Rand on the wrong paths (eg: the whole turning of the BT into what it became is Taim's doing, Rand merely condoned it, or brushed it off as something he had no time to correct), making him harder and darker and darker, frustrating him, deepening his fears of death for himself, and those he loved, forcing him more and more into battles, destructions, mistrust, hatred, his love of power and honors Etc. In the late series, Rand started to think more and more like a Forsaken, even though his goal was still to defeat the DO. He was a King, he had all the power, he was in charge and everyone had to grovel before him, and no one could stop him or refuse him, and if anyone challenged him, he would bring them down.

You cannot embrace your role as the Champion of life when you reject more and more all that it means to be a human being, when you shape yourself as a weapon to destroy Shai'tan, and try to force everyone to do the same, making yourself the greatest tyrant alive. Rand's role was more messianic. He had to show the world the LB was coming, and show by his own example that they had to sacrifice many things to dedicate themselves to the greater good, or everyone would lose everything. His own being, the miracles around him, were also to be the proof the Creator had not abandonned Creation. But Rand's faith, his belief, his understanding of his real role wasn't strong enough. For most of the series, he fell quite short of what he was supposed to be, and the Wheel wasn't able to work through him as powerfully as it needed (which wasn't unexpected, however... the prophecies are proof of that, that Rand would have a long and hard path before he finally became at the end what he had to be, and it's only through his hard experiences and reaching the bottom of the barrel that Rand could reach this point). In the end, not only Rand but the whole world had to fall into madness and reach bottom, before it understood what it faced and how to face it.

A lot of the series is about that. Aridhol became SL because it rejected its humanity and sought to destroy the Shadow by accepting all the means possible were justified to defeat the Shadow. It rather destroyed itself.

The Whitecloaks are another example. In their rabid hatred of the Shadow, they end up killing innocents more than they catch real DF.

Masema is yet another example. His faith in the Light was complete, but he fell into pure evil to force everyone to share his beliefs...

As for Rand... he's made good decisions and he's made bad ones - but most of all until his epiphany he had the wrong perspective and the wrong attitude. He couldn't be the Champion of Life the way he was. He was falling more and more in the ways of Aridhol (the victory of the Light is everything, and nothing else matters) and in the philosophy of Elan Morin (the Pattern is a prison of pain, and destroying it might be a solution). The Wheel could counter Shai'tan less and less through a man like that, and in TGS especially it was becoming evident that the Wheel had less control over Rand than before, that the Shadow was winning that duel... until Rand's epiphany.