Making a TE cooler more efficient?

[Mumbles]

Hey there, this isn’t exactly about a CPU cooling topic, but it is certainly exotic. I recently bought a $30 TE cooled mini fridge from Walmart and I’m trying to figure out how to make it more efficient. I figured I would replace the thermal grease with some Artic Silver 5, but I noticed that the cold side of the TE had to pass through essentially 4 different mediums to finally cool the fridge. The cold side was connected to a small aluminum block with themal grease, then the block was connected to the wall of the fridge with thermal grease and screws. Would it make this fridge more efficient if I placed the TE closer to the fridge wall and had the hot side connected to the aluminum block, then the block to the heat sink? Im also thinking about replacing the small fan with something more quiet as well, I believe the size of it is 80mm, not sure what to replace it with though. I’m certainly not an electrical engineer, so any help or suggestions would be great! Thanks!

[Kilrah]

Nope, it's better how it is. There is 10 times more heat to transfer on the hot side because of the appaling efficiency of a TEC, so you want that to have the lowest thermal resistance.

[Mumbles]

1 minute ago, Kilrah said:

Nope, it's better how it is. There is 10 times more heat to transfer on the hot side because of the appaling efficiency of a TEC, so you want that to have the lowest thermal resistance.

Should I still replace the thermal grease with something of a higher quality to improve the thermal transfer? 

[Kilrah]

You can, but it probably won't improve things in a noticeable way.