On 'modern' engines, a "timing belt" drives the camshaft and other assorted implements of frustration, but usually has very little to do with igniion timing. Some motors have the cam shaft driving the distributor, but cars with electronic engine management generally have some sort of induction pick-up somewhere on the driveshaft and the rogramming manages spark timing.

On a Mini A-series or A+ series motor, there is an enclosed timing chain that drive only the cam shaft. Except for modified motors, the cam timing is not adjustable. The cam shaft has a gear on it that drives the distributor shaft. The ditributor has, in very basic terms, weights and springs that modulate spark advance via centrifugal force. Most dizzies have 'vacuum advance' that is a fuel economy device that advances timing when the throttle is closed, so the engine can idle/cruise on less fuel.

Ignition timing is adjusted by carefully! rotating the body of the distributor under certain parameters to set the desired or required timing advance according to spec. It isn't difficult, but care and patience is needed.

Before timing is adjusted, the internal components of the distributor need to be in good condition - the points need to open a certain amount to provide a 'good' spark and the contacts need to be in very good condition to get consistent opening and closing. Other things like the rotor, distributor cap, ignition wires and spark plugs also need to be inspected, cleaned and adjusted first.

And before all that, the carb needs to be working well and set at the right idle speed.

And before anyhing else, you should try the combustion chamber cleaning as suggested.

I will try the techron fuel additive first. 

About the new engine - I paid cash for the car. It has very little rust and is in great condition. I plan on driving it for summers and then two winters from now ( having enough cash saved up) doing a complete restore and then 4 winters from now a bigger motor (maybe). 

Try running some Sunoco 110 leaded premium and see if it still diesels, or just use my clutch trick like I have on my 13 to 1 compression 1380 for many years. It has the added benefit of protecting your flywheel ring gear from premature failure!

But you're going to need a real engine soon anyway!  As you get to know it, 13 horsepower gets pretty boring!

As several have said, you probably have hot deposits on your pistons or heads. Those stay hot enough to ignite the fuel after the engine is turned off and there is no spark. There is a very simple but effective cure: A bottle of Techron in the tank. For really bad conditions, run it in two tanks at maximum strength. I've cleaned up many engines that way.

I currently buy their super concentrate in drums and dilute it per their industrial instructions to sell. It dramatically changes engine performance and dieseling.

Once it is cleaned up, check the timing and other things.

So I've done timing belts and the like on other cars. What would be the procedure for checking timing and adjusting lean mixture. I'm new to the mini game and this is only my second carbureted motor. Also I've been looking into the vin and motor numbers. My vin is correct for the listed year but I'm struggling with the motor number. Is it okay to post it and ask for help in that regard or is that dangerous like posting a vin number is dangerous?

Mmm Maybe maybe not, dieseling is caused by excessive combustion chamber temp. so when you switch off Ign the fuel is lit off by the hot chamber. This can be caused by a few different things excessivly lean mixture or Ign. too far advanced or as suggested excessive carbon build up. I would suggest check the basic's first ie Ign timing, mixture.

Too much comp. and bad fuel would cause pinking/pinging but not always dieseling..........

It's "caused" by too much compression for the quality of fuel being used. Carbon build up can raise compression and create hotspots contributing to the problem.  Try using premium fuel... a good idea anyway for Minis, and you can completely prevent it by shutting off the engine as you take your foot of the clutch with the car in gear!

I am the new owner of a 1976 Austin Mini with the 850 cc motor. It has a single carb on it. It is diesling when hot. My question is two fold. Is this just caused by carbon build up in the engine or is it caused by too high of an idle?  How high of an idle is too high and how do I go about adjusting it?  Thanks in advance. 

Devin