actually, that afternoon shade might well spare their lives.

they can take all the sun you can give them, it's the temperature itself that will beat them down.

but with afternoon shade, and lighter-colored mulch (this isn't a place to be using 'color me black') all you should really need to do is hose down the container to help cool them down on very hot days...

if they start fading, I highly recommend a 'sweet potato vine' in either the tri-color, or the dark purple (or both) which will take over any size container in a matter of weeks :)

I would move them. I've never dug any up, just planted seeds and they self-sow after that (weed, nice ones but weeds just the same). So what likes baking in afternoon sun? Cannas, bouganvillea, and surely many more plants that someone must have a list of....

Nasturtiums really, really don't like being transplanted, so leave them where they are. They'll take a lot of heat, actually. Here in the subtropics, where summers are truly fierce, nasturtiums are on the list of potential environmental thugs. They'll self-seed all over the place. I'm forever pulling them out when they appear where I don't want them. Just don't let them dry out.

if worste comes to worste you can always eat them and plant something else.