I have a Windows 7 laptop with an overheating problem and am looking into replacing it. I want to be able to transfer all of my files and programs to the new laptop. If the new laptop is Windows 8, I assume I would still be able to restore from my Windows 7 system image, and that after doing so I would have all of my files and programs in Windows 7 on the new laptop. Would I then be able to reuse the Windows 8 product key that came with the laptop to re-upgrade to Windows 8 and have all of my programs and files in Windows 8?

As per the description I understand that you want to restore Windows 7 image in Windows 8.
I would like to inform you that unfortunately you would not able to restore Windows 7 image in Windows 8. However as work around you can copy all your data on a eternal hard drive and then pasted in the Windows 8.
I would also like to inform you that the Windows 8 product key which you receive with the new laptop, you will not be able to use for the upgrade process from Windows 7 to Windows 8.