Right, you'll see artifacts before it starts to overheat... And with an older card, honestly, I wouldn't be all that concerned about it frying. Because, then, that would give you a reason to get another, better one!
But I understand where you're coming from. You should have no problems running it on "silent mode"... You may want to just check how hot the air is coming out of the fan. If it is just lukewarm, you'll be in good shape!