Go to Catholic Encyclopedia, click "A", and scroll down to "Abgar the Legend of"
It starts this way.
The Legend of Abgar
The historian Eusebius records a tradition (H.E., I, xii), which he himself firmly believes, concerning a correspondence that took place between Our Lord and the local potentate at Edessa. Three documents relate to this correspondence:
*the letter of Abgar to Our Lord;
*Our Lord's answer;
*a picture of Our Lord, painted from life.
I have honestly and with prayer, tried to understand why someone who I am sure was considered a good person in his time, could do some of the things he/they, did in the name of the Church.
My conclusion.
* He convinced himself that through a miracle from Christ it actually happened.
*He told himself, can we know for sure that Christ didn't really do it.
*He planted the seed, and let others harvest it and therefore felt no responsibility for the out come.
*He thought, how could anything so beautiful be wrong if it has good fruits.
*He reasoned, if this brings people closer to Christ, it justifies the means.
If you have other explanations, please enlighten me.