Plastic is no better at "generating" heat then anything else because any heat is generated by the activity of the bacteria that digest the material to be composted. Sometimes plastic composters do not allow enough air in and cause the material to hold too much moisture and the material enters anaerobic (in the absence of air) digestion which produces a very stinky mess.
If a bin is needed 12 feet of wire fence works quite well.

Anything from a simple circle of fencing or chickenwire to a plastic or wood bin will work fine. The only thing I would recommend against would be the tumbler, they are finicky and harder to get good compost from, besides being hideously expensive.

If the tumbler is out, I was thinking of using a 2' by 3' dog kennel without the floor tray. Would this be too small to build up enough heat?

Many people report having good results with a compost pile of that size, I have not. When we lived in town, on a 66 x 66 lot with a 36 x 36 house on it, a composter much larger then a 40 gallon trash can would have been difficult, to place and have enough material for. I could not get that trash can composter to do much more than anaerobic digestion, the material was always too wet and smelled terrible. However, the 4 x 4 bins we built at my parents, where we had a very large garden, would get hot and keeping the material just moist enough was easy. I have just had much better results from compost bins 4 x 4 to 6 x 6.
Then again, if you think you will not be able to fill a 4 x 4 bin you can start smaller.

I could fill a very large bin, but I am tired of failure in other parts of life, and I would like to have some composting success, or at least if I fail to have a small failure that makes less mess and won't discourage me of trying again. That's why I'm wondering how small I can go. But I don't want to start so small that failure is a given.

I noticed you asked about needing a tool to stir it. Regardless of what you use for a bin, compost will happen faster if you can turn it when the bin gets full. The easiest way is to take the bin off of the pile, set it next to the pile and shovel the pile back in. If it's been long enough there will be finished compost at the bottom of the pile.

The dog kennel thing will probably work, because the pile does not have to heat up to make compost. It will take longer if it's cooler, but it will get there.

If you feel you must buy one I'd go for the wire one. Does it have a door or is one side the door? Or as was mentioned above you could just buy some fencing hook it together in a circle and fill it. To turn the compost you can either reach in from the top and stir it around a little or remove the fencing, turn the pile then put it back to keep things neat.

If you pile things up to rot you won't fail. They will rot. Turning just adds air so things rot faster. You don't have to turn unless you want compost sooner than later.

Pile it up, get it wet as you do if you need to and let it sit. If you are going to be adding food scraps and are worried about pests you can bury them in the pile as you add them to keep that to a minimum. You may get mice and voles. I wouldn't worry about them unless the bin is right next to your house.

You won't fail with compost. It might just take longer than you expect.

Here is a link that might be useful: something like this (not my picture)

You can't 'fail' at composting jamies - so don't you dare even start thinking like that. You could pile up any amount of garden and kitchen rubbish somewhere, go away for a few months, and return to find compost. Lots of people on this forum are serious about their ratios and temperatures because that's what they like doing. Or you can be like me - pile up whatever comes to hand on one side of a two bay pallet bin, poke with a fork if I feel like it, or not if I can't be bothered. It never heats up and I rarely ever turn it. When it's full I start the other bay. By the time that's full there will be something composty to shovel out of the first bay. Whatever is not decomposed just goes back in. This 'system' has served for many years and I don't see my garden piled high in 'failed' compost. In fact over here it is the standard approach - people tend not to fret over rot or turn it into a 'project' As the ads say 'Just do it'.

Well, Florauk, I like your style.

My first and only attempt was about 25 years ago.

I recall a chest high pile of slimy leaves surrounded by a rippling, falling over home-built enclosure of wire.

With the kennel or another bin I have conquered the surround. I thought I had to stir in order to avoid the slime. Since I'm not strong in the back, I wanted to go as small as possible.

I'm also impatient.

I hadn't thought about the voles and mice either. Now I'm thinking I need an enclosed plastic thing for the peelings and the kennel or kennel-like thing for the yard waste.