JayP's right. There shouldn't be any reason to run hot water to the fridge.
If you're installing an icemaker line, you need to tell us what kind of water supply piping your house has. You'll tap into a cold line for this purpose, not a hot.
If you have 1/2" copper, most home centers sell kits with everything you need to install a line. This kit will include a saddle valve that pierces the copper line (very easy), tubing, and all the connectors you'll need. If you have another type of plumbing don't panic, we'll talk you through it.