Make sure that if you are wanting a clean fuse, you make sure that the beads can “breathe”
Make sure to put something on the medium/heavy side on top of your perler immediately after fuse; if you don’t, the will warp at the edges, and you will have to heat it back up to get it to lay flat again. I’ve seen other people use heavier items like dictionaries, but I don’t see the benefit. I’ve had success with DVDs and smallish books.
If you can, take your creation off the pegboard before it’s cooled (don’t burn your fingers!) and lay it on a piece of parchment paper, give it a few passes with the iron to heat it up a little before putting another piece of parchment on top, and then applying the weight.
It doesn’t take much weight, all you really need is a couple of DVDs or books. 15-30 minutes should be fine to let it cool.
If you are just moving a board that you have made from one room to another, you just have to be careful as you walk.
If you need to move them longer distances, I have found that it works really well if you take a second board, line it up on the top, and tape it down with masking tape.
I start by taking one corner, taping the top, and then sliding it to the edge of the table and taping underneath, and rotating it 180 and getting the diagonal corner, and then just repeating until it is secure. When they are solid like this, you can even transport them vertically. When you get to the place you will be fusing them, you can just cut it with an exacto knife.