Using tmpfs + a very large swap partition for /tmp instead of a regular filesystem?
This is NOT A Good IdeaTM.
You'll be fine with a large /tmp partition, mounted like this (from your /etc/fstab)
tmpfs /dev/tmp tmpfs defaults,nosuid,nodev,noexec,noatime,nodiratime,size=6000M 0 0
And you could add your external drive as a giant swap partition
/dev/sdb1 swap swap defaults 0 0
When that hits its limit, your machine will start to swap the pages from RAM to disk - at which point, load averages will go through the roof and the machine will grind to a halt.
Its a bad idea to rely on SWAP in any way, you'd be better off selling your 500GB drive and simply buying more RAM - its cheap.
In summary
If you really want to use your 500GB disk, you could mount your 500GB disk on /tmp with a non-journaled filesystem with atime and diratime disabled (eg. ext2). That would be substantially faster than dealing with a machine that is SWAPing
This could be a reasonable idea.
Putting an actual filesystem on /tmp does incur overheads, because filesystems go through great lengths to make sure that the data on disk is not corrupted in case of system failure. For a /tmp that is cleaned at boot time, that is obviously just overhead. Using a tmpfs would avoid that overhead.
On the other hand, filesystems also make sure that files are organised on the disk in a way that optimises access time - i.e., they will avoid fragmentation. Typical sequential file accesses will (mostly) result in sequential disk accesses, which are more efficient than random accesses. This effect is more pronounced on spinning harddisks than on SSD. The swap+tmpfs combination can't easily do this, because swap is not aware of which piece of memory belongs to which file and tmpfs isn't aware of how pages are mapped to physical memory or to the disk. For large files, however, it should work well, since both tmpfs and swap try to keep things contiguous in that case. At least, as long as there is a lot of free space on swap (otherwise fragmentation kicks in), and writes happen slowly enough that they get a chance of being swapped out.
So the bottom line is: it depends, you should try both options to see which one works best.
When you mount the tmpfs, do remember to set the size explicitly. The default is half the physical RAM, so just 3GB.