P38A Painting the Transmission Fluid Sump

I've been doing a bit of preventative maintenance before the winter, and just fitted some new transmission oil cooler pipes when I noticed the sump has a bit of surface rust, probably down to me leaving the acoustic cover off last winter so it would have received a fair amount of salt spray.

So question is whether there's any good reason not to paint the outside of the sump? I was thinking of using POR15 and top coat. I don't think the sump gets excessively hot, so hoping that should be ok. Anyone got a better informed opinion?

The sump also aids in cooling of the oil, but I cannot really see a reason not to.....

+ 1 cant see what difference it would make.