Peltier coolers will move several watts of heat from the cold side to the
hot side but you do need to make sure that you have a big enough cooler to
do the job.
Insulating the enclosure will decrease the amount of heat getting into the
enclosure and this helps allow the device to work well. Look at the car
cooler for how much insulation that you need to really get a decent
temperature drop. IN addition, you also need to be able to remove the heat
and cold from the peltier device or you will be making a cold spot that
really doesn't cool the whole enclosure.Water (actually antifreeze) pipes on
the cold side have the problem of often freezing water as a single stage
cooler can easily hit temps that low if there isn't a lot of heat input to
the cooler. Also, removal of the heat from the hot side will increase the
efficiency as the coolers work better at low temps than at high temps in
addition to the fact that they produce a diffeerential of temp across them
according to the current tht is run through them and the amount of heat that
is being movrf.
I like to run my coolers at about 50-75% of their capacity to keep them at
their efficient range. I'll note that you can run several peltier coolers
in series as long as they are of the same type device - junction count
doesn't care but the individual junction type (peltier devices are made up
of a large number of individual pellets of the junction material). This can
make the construction of the power supply a lot easier as lower currents can
be had which reduces the size of the parts.
Basically, insulate well, move the heat quickly and run enough of the
devices to move all of the heat you do have to move. If one won't do the
job, add more and eventually you will move enough heat to cool to the temps
you want.
I've made some stacks (cold to hot sides of several devices, each lower in
temp of the stack a smaller size) and gotten temps down below -40 with these
devices.

--
Why isn't there an Ozone Hole at the NORTH Pole?