During hot spells, I have found that when I start the engine at the hottest time of day the starter doesn’t shut off right away when the engine starts. I have to shut the key off a few times before I can get the starter to function normally. Is the heat causing the engaging gear to stick?
First request would be make, model, and year, so the full time motorheads can see if there’s a known problem.
Absent that information, I’ll hazard a WAG that the Bendix drive is hanging up. Whether that is a DIY repair depends on many things, but starts with the info up top. 
Maybe there’s a frog in the Bendix.
It’s a 1984 Ford T-Bird, V-6 engine. (Engine replaced June 2001; all major components of ignition system replaced in last 2 years.)
Thanks. That should help Gary T or Rick with a more precise answer. I’ll stick with my original WAG and suggest that you call Pep Boys or another auto parts chain to see if the Bendix is available as a separate part. It may not be, in which case you’ll have to either drop a whole new starter into the car, or take your existing starter to a starter/alternator rebuild shop (assuming you can locate one).
From the description of the symptom, it’s a pretty safe bet that something is warping or swelling from heat. That something is not necessarily the starter drive (Bendix) - it might be related to the armature shaft or its bushings. I think the wisest course would be to replace the starter as a whole.
I’ll add that the replacement starter should be properly shimmed. (rule of thumb, there’s a paper-clip’s worth of gap between the flexplate and drive gear when extended.)
A good replacement starter will have a shimkit. Remanufactureed starters will often be machined to remove warpage of the case and the shim kit permits proper function.
You do NOT want it to tear up your flexplate/flywheel. Considering that part is pretty much dead-center in your car, it’s a PITA to replace.
Ask me how I know. 
Only if it’s a GM starter that actually uses shims. The great majority of cars don’t.
How many starters are being built that a driveway mechanic can readily break down the starter and replace just the bendix and/or solenoid? (Not to mention availability of sub-parts at the neighborhood parts store.)
As one data point, the shop manual for my Dodge Ram says “All of these starter motors are serviced only as a unit with their starter solenoids, and cannot be repaired. If either component is faulty or damaged, the entire starter motor and starter solenoid unit must be replaced.”
I also strongly advise replacing the entire unit or having it rebuilt. Car parts seem to be designed with pretty well-matched life expectencies. If you tear down the starter and replace the solenoid, the starter motor itself will fail two weeks later, just to annoy you.
The last starter which I remember rebuilding was in a 70’s something Chrysler belonging to a buddy. The engine was either a 170 or 225 slant six, but sufficient space existed to remove the starter from over the fender. We spread out newspapers and put in a new Bendix and solenoid on his kitchen table. His wife came home before we were done, and was displeased at the sight.
IIRC, the cost difference between a Bendix and the reman starter for my 85 Ford was so small, I went with the reman unit.
Thanx