I have an SSD and a spinning disk. Windows 7 is installed to the SSD, but I have the temporary directory pointed to the spinning disk. I have a replacement for the (quite old) spinning disk. I am going to boot with SystemRescueCD and clone the old disk to the new one. What do I need to do to make Windows recognize the new disk as the old one before I boot Windows again?
Are you just worrying about the drive letter? You can install the disk, and if Windows gives you a different drive letter than you wanted, you can change the drive letter in disk management.
Just go start > run (or search) for diskmgmt.msc
Right click on the drive you just installed, and select Change Drive Letter and Paths...
I don't think it is a problem to boot Windows with an invalid temporary directory. I've toyed with having the temp folder on a RAM drive before and it did not complain when it was not there. Windows will ignore it until needed or reassign it to the default on C:.
With some luck, windows will give the same letter to your new drive if it's the next available letter (eg D: or E:). Just verify any pointed directory afterwards.
If you want to really be sure, boot your computer with your current drive unplugged and see what happens. In case of problem, replug it and modify your settings.
Edit: Thinking of it, why don't you boot with both disks running. Unmount the drive and map the new one immediately? I am pretty certain this will work just fine assuming no application is using the Temp folder. That said, I still think a plain reboot would work well in most situations.