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If the wife wants clean, then you can't do cleaner than one of those immersion heater things that plug into the cigar lighter socket. The only trouble is that they take about 20 minutes to boil one mug of water. I keep one, together with a few sachets of coffee, sugar, powdered milk etc. in an old biscuit box in the Jeep. But I also have a petrol stove in there, not to mention one of the Aldi drainer hobo stoves. You can safely use an immersion heater in the car with all the windows shut, which doesn't apply to any other stove that I've come across although I've got an Eberspracher heater thingy in the truck.
Next cleanest after electricity is gas or meths, with gas edging out meths on convenience. Either of those will be clean enough for almost any wife but you're right to be concerned about the temperature of gas cannisters in a car parked out in the sun. Any of the Trangia, Tatonka, and a whole bunch of other meths stoves including the various DIY coke can varieties (some of which definitely won't suit many, er, domestic arrangements) will make you a brew using something like 25-50ml of meths. Be aware that the meths flame is a feeble thing compared to the flames you get on pressure stoves, so a windshield of some kind is usually essential. Also be aware that the meths flame is almost invisible so it can be more dangerous than you might think. Meths stoves need almost no priming, but the gas wick types (lots of little holes) need time to heat up and 'bloom' to get the most heat out of them. It's harder to adjust the flame output with most meths burners than with pressure stoves (gas and petrol).
White gas (Coleman Fuel) in a pressure stove is nice and clean, and aviation spirit comes a very close second. There's practically no residual smell like there is with unleaded petrol, paraffin, diesel etc. and you can fall back to unleaded petrol in emergency. Unfortunately Coleman Fuel is one of the more expensive ways of buying energy.
Unleaded petrol, paraffin and other liquid fuels are to be avoided if the wife is on the fastidious side. The worst problem in my opinion is the nasty smell if you spill it, which is very hard to get rid of especially on fabrics. You need very good ventilation with any road fuel used for cooking. You can work cleanly with them if you have enough experience.
Solid fuel tablets are relatively expensive but they're easy and clean to store, they don't accidentally spill and they don't evaporate away while you're not looking. They don't burn especially cleanly and they can smell pretty bad. The stove itself is just a bit of folded metal or a couple of bricks, so the cost is minimal.
Finally wood. Forget it in this application. Filthy dirty, even if it is free. I use a Ghillie kettle a great deal (similar to a Kelly kettle). Fantastic for the job they do (boils 1.5 litres of water in five or six minutes with little more than a handful of twigs) but you need to be prepared. If you aren't prepared (with carrier bags, leather and plastic gloves, generally ways to avoid getting covered in soot and ash) then you're going to get dirty. Same with Honey Stoves, hobo stoves and other wood burners unless you put a meths burner in them which has always seemed pretty pointless to me.
My personal favourite all-round is a pressure petrol stove like the Optimus 111B. I run mine on my own secret mixture of brake cleaning fluid and dodecane (kind of like clean paraffin). I prime it using meths, which makes almost no soot. That way the burner is so hot that it produces a blue flame immediately it's turned on. Boils a small kettle of water for a brew in about four minutes, which is about 16 grammes of fuel. The tank holds about 400 grammes. The whole thing is in a neat box which you just open up to start cooking, but the lid doesn't open right back so there's a limit to the size of pan that you can rest on there. For my 28cm frying pan breakfasts I use the Optimus Nova. There have been quality issues with the Chinese-made Optimus products and I'd recommend sourcing an older used one if you can find one in good condition. I once owned an Optimus Hiker Plus for about three days before sending it back to Amazon as a hopeless case.
There are some stoves which will burn both gas and a variety of liquid fuels, including petrol and diesel but usually not including meths.
