I disagree that your issue is typical. If you have a known good battery that is fully charged and all the other components are working properly you should not have this issue. Over 5400 miles on my car and never had this problem and I’m still on the original battery!
That being said, in order for you to figure out what the problem is we look at it from your post. When the car is cold it starts and runs just fine. Only after the car has been running and comes up to operating temperature you have the problem. This is telling me the issue is heat related. From experience I would be looking at the starter itself. The only way I know to test it on the vehicle is to do an amp draw test. Typically the starters will draw about 250-300 amps so if yours is drawing more then the starter is your problem. If you are not sure how to do the test properly or don’t have a reliable means (equipment) to do the test, find someone local who can. Often times the windings or brushes inside the starter break down, causing high resistance. This resistance causes the high amp draw that your battery cannot overcome. Putting in a bigger battery is just a band-aid at this point.
This advice is predicated on a few things. First, you have not made mods to the engine and have the factory tune. Second, you have properly inspected and verified the wiring from the battery to the starter solenoid to the starter and the wires are tight and not corroded, etc. Third, you have inspected and verified that the battery and associated chassis grounds are clean and tight, with no corrosion, etc.
In rare instances, the starter solenoid can be the culprit and is much cheaper to replace than a starter. If you happen to have a buddy that would be willing to loan you his solenoid for testing purposes after you have checked everything else try that but what you are experiencing is not to be considered normal in my opinion. Good luck and let us know what you find.