There are some threads on this in the equipment fourum area that might help.
The best way is "direct" to an isolatable (deep cycle) second battery with heavy gauge wire, #10 or better and with an in line fuse rated per refigerator manufacturer specs (and they ussually include them with their fridges.)
On the other hand, I have run mine off an "always on," non ignition switched cigarette lighter with complete success, though with a cheap 12v extension cord/cut off switch that kills fridge power at 11v. I'm currently running mine that way and its been more than a year of continuous use with no issues, with a 16qt Engel fridge and one grp 31 Blue Top. I have been getting about 2 1/2 days when temps are high 80's and 90's before the switch kills the fridge, that with a four door JK with a black top. I don't recall the fridge being shut down when temps are more moderate, but I try to run the Jeep every so often (and its hard not to since it so much fun to drive.) I've run a 60qt Engel Combi the same way, but not for extended periods.
A test will be coming up when we head to Easter Jeep Safari since we'll try running my 16qt Engel and my 35qt Engel both through one spilt plug, and an extension cord/cut off switch each.
BTW, you pretty much need a deep cycle battery to run a fridge for more than just when you're driving. I've run one on a starting battery, but it's a mtter of getting it cold when you're driving and then shutting it down when you're stopped. No substantial run time shut down.
Two batteries is far better than one, but I have no room in the engine compartment and can't find room underneath either. I am trying to avoid sacrificing interior space but may have to to run two fridges.
JPK