Crucified in his Undies

A local church near me erects a cross every Easter adorned with a crown of thorns and Jesus’s unraveled underpants.  The latter is the bit I don’t understand.

The Romans put a crown of thorns on his head, beat him and spat at him.  They nailed him to the cross and stripped him down to his undies.  Why strip him down to his undies?  I presume it was probably a hot day and Jesus was an Olive skinned man, it’s not like he would have been sun burnt, if anything this would have improved his tan.  And if they were doing it to shame him why not strip him totally naked?  If they really wanted to make him uncomfortable why didn’t they make him wear a massive duffle coat or summat?

"Cross c/w Crown and Undies"
(There's a pub nearby, maybe they should rename it to the "Crown and Undies")