It's probably not that hard.. a simple modification to the door buttons I'd imagine. It might even be an off the shelf part.
However, 365s don't have air conditioning. In the summer, you'd want those doors kept open. In the Winter, you'd want them closed - but a fair few people do board on a cold/wet day and shut the door behind them (more so in rush hour than at a weekend with people who probably don't even know you can shut them!) so it isn't that necessary.
When they get their refurbishment, they may well get new door buttons because I believe the buttons are positioned as open (bottom) and close (top) and now I've seen on here that it's meant to be open (top) and close (button)... rather like the older trains had it before the rules changed, presumably so people in a wheelchair could reach the open button (and not necessarily have any need to press close at all).
Given the known issues with the doors on a 365 though, I am not sure you'd want the doors closing by themselves - they'd probably hurt people who boarded while they closed. I've 'tested' them using my foot, with strong shoes, and you don't want them hitting you to detect an obstruction!