1. Put masking tape over the data and electrical connectors of the drive.  
2. Immerse the drive in a ziplock bag of minute-rice, with the data/power connectors sticking up. This can't be regular rice, it MUST be minute rice. This acts as a poor man's silica gel later in the process. Close the zip-lock.  
3. Freeze the bag of rice with the hard drive in it in the deep freeze for 24 hours. You want it completely frozen, patience is a virtue.  
4. Remove the bag from the freezer, and take it to a pre-prepared computer where the drive is ready to be received and plugged in (longer data cable, longer power cable, etc...) You should have another big data drive in the system ready to receive the data from the frozen drive.  
5. Leave the drive immersed in the minute rice except for the data/power connector. Remove the tape. Plug in the data and power cables. Try to re-seal the zip-lock bag as much as possible so you don't have rice grains escaping.  
6. Orient the drive so it's laying in as natural of a position as possible with as much frozen rice around it.  
7. Fire up the system, and try to access the frozen drive. This is the moment of truth. If you're lucky, it'll identify and respond, and you'll have access to the file system.  
8. You now about 20 reliable minutes to copy data. You may get more if you're lucky. Copy copy copy. Note: The drive WILL be slow at first, and will speed up as it starts to warm.