DIY submersion chiller not evenly cooling?

[Paradigm]

My housemate and I made a DIY chiller using a water reservoir inside a fridge to cool tub of water that our carboy sits in. We have gotten it down to 12 C (53.6F) as a test of maintaining below room-temperatures and the part that is touching the water is at 12.5, but the top is at room temp (16.5). This is just a est run with a carboy full of 5.5 gallons of water.

The water only goes up about 4-5 inches of the carboy, but from what I know about liquid physics, shouldn't all of the liquid inside be 12.5? Does it just need more time?

We can't have too much more water because with more water we don't have the power to drop the temperature enough with my small mini-fridge.

 

[acidrain]

The fermenting beer will have plenty of convective current, so that won't be a problem.
Are you going to use some kind of controller? If so, you may need a valve that closes off the flow of cooling water, otherwise the natural convection of the chiller water will continue to circulate without the pump. Weird, but true.

 

[Paradigm]

We have a pump that pumps cold water from the reservoir into the bath, as well as a heater that can warm the water. We have two tubes, one attached to a pump and one just full of water / submerged to keep the water levels even with atmospheric pressure. We have the pump and heater hooked up to a temperature control unit that turns on at +/- 0.3C difference in target temperature.

Currently we are using it to maintain 19C at the bottom of the bath (21C at the top) to do a warm finish of our primary fermentation in order to get the FG down to where we want it.