If you have two remote locations in Transmit 4, say an S3 and an FTP location, and you move a file between these two locations, Transmit will automatically download that file, and then upload it.
Where does Transmit 4 store these temporary files?
You can find this out by yourself:
This will list all created/opened files, it shouldn't be difficult to identify the temporary files.
The opensnoop program is remarkably useful, but to answer the actual question in case somebody is in a quick bind, for Transmit 4 the location of the temporary files is:
Transmit appears to clean up after itself within a second or two of the upload completing. The name and path of the folder implies to me that the system might clean it up if Transmit doesn't get the chance.