'Think' gets my vote, especially if you use the "if [he] thinks...then..." construct. But I've always thought 'think' was the more correct usage.
However, I honestly don't think either word would cause the reader to stumble or jerk him or her out of the story. Enough people have seen and heard 'thing' used in that context that they're used to it, so I doubt you could go too far wrong either way
Caroline
