Here's another possible model:-
Hello Andy,
Sorry to read your child has special needs. Freezers and travelling hmmm.
There are some dedicated portable freezers such as this 18Litre one which uses a compressor like your domestic fridge/freezer at home.
http://www.waecofridges.co.uk/freezer/cdf18.htm
Compressor fridges & Freezers are the norm for domestic use, where the slight noise they produce is not a problem, but in touring caravans, the noise of a compressor could be quite distracting. Consequently most caravan fridges use the virtually silent absorption method, which as the benefit of being multi-fuelled.
Compressor systems are generally more efficient and this is demonstrated by the power consumption of this unit.
The information on the web site is not very clear, they do not tell us what the dc cuurent requirement is to power it, but they do give us some information which I might hazard a guess will give us the power needs to maintain the freezer function.
Apparently the the internal temperature can be set between +10 to -18C. They claim a power input of 36 Watts (which is 3A @ 12V)
and they tell us to maintain +5 with an ambient of 20C uses 0.38Ah
and to maintain +5 with an ambient of +32C uses 0.64Ah
Without repeating the calculations here, As a rough estimate the unit is capable of dropping the internal temperature by approximately 30C from ambient with the compressor running continuously, so it theoretically could keep the freezer -18C in ambient temperatures up to 12C. There after for every degree rise in ambient the internal temperature could rise by the same amount.
I have to observe the current consumption is surprisingly low Circa (3A)compared to a normal caravan fridge that will use about 8A, so its quite feasible to run it in the car boot, but its is still quite a substantial continual power drain, so it would not be wise to leave it running form more than about 5 to 8 hours without the engine running, other wise you may not have enough battery power to start the car.
Hope this helps