Engine week at stat up

I have a 2001 Buick LeSabre (Limited), with 101,000 miles. It runs great and a very reliable car except:

After going for some driving in town during a warm day (60 F or above) doing business, the engine gets warm but within normal temperature range, and after making a stop to get groceries for eample, I have to be very careful when starting the car again. If I let the starter go for more than a quarter tourn (crank), the engine gets week and acts like it is flooded with gas, just like when we had carburators in old car and it dies after a few shakings. So I have to wait for 15 minutes at least before I restart the engine but doing so I have to be really careful again not to let the starter crank for more than a quarter turn. However, this problem does not happen during cold weather days (say below 40 degrees F). What is going on with my car?
Thanks.

What Happens When You Hold The Accelerator Pedal 1/2 Way To All The Way Down Prior To Cranking On A Hot Start (Letting It Up Immediately If The Engine Starts, Of Course) ?

Has the "Check Engine " light illuminated ?

CSA

one thing to check would be the catalytic converter. when they are old or are breaking down, And when hot the have a tendency to start to clog up. My grandmas buick had this problem you could drive do errands and same issues you are having. i replaced to converter for her and no issues since. Im sure if you take it to an exhaust shop they can check this for you!