Thornmail is worthless
Edit: Worth Less than every other possible option
First, a stat and gold breakdown: Not counting its passives, Thornmail is only 74% gold efficient. Compare that to Randuin's 78% (not even counting the crit reduction), or Sunfire's 80% (not counting the fact it deals more damage and doesn't require the enemy be auto-attacking you), which both cost the same amount.
Thornmail provides only 450 total Effective Health compared to Sunfire's 680 and Randuin's 640 Pretty big difference in base stats for items with the same cost, both more gold efficient than Thornmail.
Now, let's look at the passives: Thorns -- No longer reflects damage based on the damage of the attack, so you need to have your own 90% increase (Rammus) to make it enough damage to be worth buying instead of Sunfire. +Grievous Wounds -- Great, if you have a way to force the enemy to auto-attack you. Otherwise, it's almost pointless to have a method of applying GW that the enemy is the one in control of. Cold Steel -- Most importantly, this actually counters the other passive. The slower the enemy attacks, the less damage you deal with the item. Might be pretty effective if you could stack it with Randuin's and Frozen Heart, but it's unique and anyone it might effect is likely building crit chance anyway, so you're better off with Randuin's.
There is only one champion that can purchase it effectively even among those champions who scale armor themselves: Rammus. And he has basically exactly the same damage on his passive plus a 50-90% increase in armor for it to scale, along with a taunt to actually make an enemy attack him to apply it at all. Compare that to Malphite and Taric, who should be able to buy it effectively while stacking armor, or even Shen and Galio who should be able to use their taunts for it, and it simply doesn't deal the damage it needs to to make it an efficient purchase. On every single one of them you'd be better off buying Sunfire and Morello to continuously apply GW to everyone in the area, since they all also scale more AP than they do armor.
You can discuss possible solutions for this in the comments. I think changing it back to a percent of the incoming damage would be a big help, and/or giving it adequate base stats, and/or replacing Cold Steel with a form of Grievous Wounds application that you can actually control yourself without a taunt.
Ok. 
