Oh I never actually thought about them baking in the sun, good job for saving them

. Yes you can pick them up be careful of course because they're young, but when you pick them up its better to pick up frogs in a non-pinching style where you never squeeze them but instead scoop them up or something. I catch these little guys in my pond every year so I'm used to handing all kinds of frogs. Out of all frogs I believe tree frogs are the only frogs that don't mind being handled and adults will often just sit on your hand content. Toads on the other hand often whimper while trapped inside your hands lol.