It wouldn't but the plastic caddy's are more hassle to deal with. I'd advise on spending the extra and getting something with quality in your laptop. In fact the metal is actually aluminium which is sturdy and if the SSD does produce heat it'll dissipate it better. To add if you look at tutorials where people bought the plastic or metal caddy's with rubber inserts, they learned their lesson and mentioned that people should get the metal construct version.
Just to be sure, you may want to pass on a link to the caddy you're looking at and the make and model as well as the SKU for your laptop.