In our previous house, the ceilings were at 9' height. We bought the tickest 4'x8' sheets of insulation board and covered them with warm and white (spray glue lightly to the plastic sheeting). Attaching them to plaster walls was difficult and overkill-so I won't cover that.
Our current house has 8' ceilings and there's carpet on the floor. The boards have been in place 4 years & I have a lot on them. They're not attached to the wall. The foot is placed on the carpet against the base board. Then they were arched to get the top in place (once in place they're flat) next to the wall. Push pins, that's right, just 1/2" push pins in the ceiling (I think there's 4/4' board) keep them in place. There's also one that is a single board on a 4' wall. It bowed out in the middle so it's held in place with a piece of selvage pinned (again with push pins) on each side of the board. At first I thought they'd fall, in 4 years they haven't, I use them all the time. They are so light weight, it's not likely they'd hurt anything even if they do fall.
Blocks stick very well, unless the fans are going, then they're pinned. Once there's about 3 block length, they don't always stay in place. With the insulation board, its easy to pin them.