What device should I buy to cool liquids in a container
You can use a "Peltier effect" cooler of the sort that you get in 12V powered portable refigerators / chilly bins/ eskys / ... . You can ither use an existing bin as the source or you can but Peltier effect devices from surplus and electronics suppliers. As you would then need a fan + heatsink + 12V power supply a complete bin may be cheaper and would be easier.

HOWEVER - it seems likely that the loss of effectiveness you are perceiving may not be real or may not be major. Another effect may be occurring.
 I say this because the very major part of the cooling from 
such a device is supplied by the "latent heat of vaporisation of the water and the actual heating of the water as a liquid should be a minimal part of its cooling effect.

Energy required for heating water or for vaporising it is measured in Joule = Watt seconds.   

The energy involved is


About 4.2 Joule per cc of water per degree C heated.
About 2260 Joule per cc of water when evaporated.


If you heat 1 cc of water fron 0c to 100 C you require only 4.2 x 100 = 420 Joule but you need 2260 to vaporise it. 

If you heat your water by say 30C then you remove 30cc x 4.2 J/cc = 126 Joule/CC
 but this is far less (~= 6%)
  than the 2260 Joule needed to evaporate 1 cc of water 



INTEREST:

It requires 2260 Joule to vaporise 1cc of water.
 As there are 3600 seconds in an hour  it takes
 3600/2260 =~ 1.6 Watt to vaporise 1cc per hour or 1600 Watt to vaporise 1 litre/hour.