I decided to start a page of updates about my 73' DT3 instead of posting them individually as I have been doing.  I got the bike fall of 2020 and have switched half the cables, redid carb, and got an all-new seat. As well as did the brake shoes and general cleaning.  Yesterday I put the seat and tank on for the first time since January and it started well.  For my first seat assembly, it went pretty well but man do you have to pull on that leather. 

Now for the issue... there's always an issue hahaha.  As I said it was running well but it was idling low and would die every once and a while.  So when I took it out today I adjusted the idle and off I went... after about 10 minutes of smooth riding the engine revved really high while slowing down.  Now normally this wouldn't be a huge concern as I would just think it was a bad idle adjustment but this has also happened to me before and it results in me having to hit the kill switch. 
Also it would not start for about 10 minutes after it happened and when it would start I could adjust the idle so it would be around 3000 RPM and then it would slowly die from there. I am just wondering if this sounds like anything other than a bad idle adjustment?

Only a guess but sounds lean by your description. so you crank the idle screw in a few turns to try & overcome that but it then doesn't want to slow down--or not slow down in normal fashion & hangs on. Idle mixture is usually around 1.5 out from seated. Screw it right in lightly seated & see if it richens it up or does little. Might be time to go through the carb & pull the pilot jet & look at the number. Might be more causing it than that though like an air leak or crank seal but first things first. Idle mixture, the one on an angle, should respond so you can hear it go rich when right in or getting lean if you screwed it out say 3 turns. If it won't go lumpy rich when right in then you have a problem--very low float level, undersize pilot jet, can't be the small Oring or you'd have the opposite affect & be chasing rich running.

First thought sounds like a classic air leak symptom.

Also check the fuel cap vent to assure air can get in the fuel tank to replace the fuel that's used.

How do you go about checking for air leak? I don’t think it is anything interior on the carb as I just changed jets and o-ring. I will play around with the settings on the carb after work today and see what I can figure.

Also, I know my exhaust pipe leaks exhaust out at the engine mount point... could that contribute?

No an exhaust leak will not effect it. The best way to fix it is to start at the airfilter. Replace all gaskets, and seals till you get to the crank seals. Me I would replace the gearbox bearings and seals also. The carb should only have genuine Mikuni parts from someone like Jets R Us. UNI airfilter cleaned and oiled. You might have an air leak around the reeds or base gasket as your problem happens when your motor gets hot?? Check if it happens with the gas cap open. Service the petcock also. It's just better to do everything cause its old and needs it. While your in there .......Check your flywheel for up and down movement with your hand. Does the motor knock at idle. Putting a dial gauge on top of the crank measuring sideways movement is a check of everything connected. Check the piston clearance with telescoping gauges These checks are worth the effort. I have covered just about everything. By checking everything you will know the condition of the motor and if it needs work. Tools are cheep these days. These are simple machines. They are treasures and worth looking after and keeping.

I have a DT2 with a standard piston and everything is in speck 49 years later. Amazing, strong bikes. This is how you use a dial gauge.   

Thank you! I'm sure I will be needing this but I hope maybe some more tinkering with carb settings will hopefully sort it out.. maybe.  My carb parts are all Mikuni that I replaced.  The problem seems to occur after it has been running for 10 or so minutes but not every time. Its looking like I am going to have to do some studying on engine work 

Update:  I reset the idle and mixture screw back to what the manual states.  At first, it would start for a second and die right away.  It didn't seem to matter if I had the gas cap open or not but there's a picture of that below.  After adjusting the idle I could get it to stay on for about 20 but needed some help with the throttle.  Too busy tonight to dig anymore but some progress I suppose.  Also my new headlight I installed looks and worked great for the few seconds I got to see it operate!