Tire Rack sells the tires separately. They’re not easy to find.
AFAIK, this is only an issue with AWD cars, or ones with traction control.
On an old, 2WD vehicle (like my 200 F150), you could use a spare tire forever with no issues (for the transmission / differential).
Most of the reports of damage are from Subaru owners, where the AWD got overheated due to the traction control thinking that one tire was constantly slipping.
I’ve always heard that you should rotate tires around so that you are not using your donut on your driving tires.
Thanks.
My last two AWD cars have a button on the dash to disable the traction control under specific conditions. I will have to look in the owner’s manual to see if riding on the donut is one of those conditions. I would think Subaru or other manufacturers would be clear about the risk to your transmission by using the donut, and have a more elegant solution than adding/removing fuses for disabling the AWD feature that is at risk.
I agree that this is more of an issue with “modern” vehicles that have traction control and AWD. My issue occurred on a Nissan Murano with AWD and CVT transmission. It was fine cruising along at highway speeds until I got into town and started using my brakes. Then the high temp transmission fluid warns started showing up. Which is one of the reasons I question wheel diameter being the only possible cause. Wheel width would be a factor in TCS systems. So I’m thinking both are a factor.
Would still like to see a good cite that explains the issues with donut spares that includes technical details. With pictures would be nice. 
Responding in general. This is one of those questions that gets me all riled up, when you can’t get a straight answer because everyone is covering their own ass and giving you a “safe” answer.
But like… here’s a spare tire after 950 miles.. It’s perfectly fine. Tires get up to temp in a few minutes, so if it hasn’t overheated after 5 miles, it’s not going to overheat after 500. They’re not going to detread, or pop, or wear down to the cords. You could, in all reality, drive thousands of miles on a spare tire before noticing any noticeable degradation to the tire itself. Sure, it doesn’t have quite the same thermal mass as a regular tire, and it’s compound and construction were chosen on the basis of cost, cost, longevity, and cost, in that order. But it’s not like you’re driving around on a party balloon that could give way at a moments notice.
Again, the real problem is that space saver spares provide almost no traction. They’re not good tires. And having 1 corner of the car dramatically looser than the other 3 is a safety hazard in and of itself. That’s why “Get off your spare tire ASAP” is, IMHO, much better advice than “Don’t drive more than 50 miles.” 50 miles is a long time where nothing bad will probably happen, but if it does, you’d want 4 good tires under you. People should read 50 miles as “Don’t drive around for weeks trying to save money,” not as a free pass to drive 49 miles and then replace the tire.
I ask for a cite because this is Factual Questions and we deviated from the OP about how going over 50 miles on a donut is bad for the car, not the donut itself.
I would think this is a factor too. As mentioned previously, many donuts are not up to full pressure if they sit in the trunk unchecked for a few years. Being smaller, it’s more weight on the (smaller) tread area, possibly more flex on the sidewalls as a result, and ignoring the transmission issues (which we shouldn’t) it is likely to flex the donut’s sidewalls more and overheat (hence the 60psi recommendation, and lower speed). Those guys with a oversize bulge where their tire meets the road are a sidewall blowout waiting to happen. If you touch your sidewall and it’s more than moderately warm, you likely have a problem coming…
Also differential traction “grab” and braking, which can lead to handling issues and further problems. All the more reason for everyone to CYA when making recommendations.
I had to use my donut a few months ago. The tire wasn’t symmetrical with the others, and I got about 10MPG while I had it on. (My gas gauge automatically posts this.)
A 50 mile limit is probably put in there as a lawyer type thing. You could absolutely ride on it until it wore out, but because it’s much smaller than the other 3 tires, that would mean the car would not handle very well and could lead to an accident. That possibility exists on any drive much over 30 mph or so. Even 50 mph sounds too fast to this hot rodder. The car is designed to use tires that are of a specific size.
My guess is that the system in your car that estimates the MPG was thrown off by the donut spare.
Possibly, but it didn’t ride correctly with the spare on.
the worry is not one of the donut crapping out on you after 50 miles (it is a real tire, after all) … but…
… since its way thinner, it has less rubber on the asphalt and less max. braking power (compared to the other 3), and cars with ABS (pretty much any newish car, today) … will “by design” reduce the applied braking power if a tire locks up.
so your donut will lock up way earlier than your other 3 regular tires and your brakes will only work at 70% *) of their potential - which is way more of a REAL risk than a donut blowing out after 51 miles of usage.
*) the 70% number is completely pulled out of my arse, and just inserted for your reading pleasure and general understanding.
I was so expecting that to be something from Top Gear in the Hammond/May/Clarkson days, but I was wrong.