A few general thoughts first, then some specifics to the original post....
I think the first thing people need to recognize is that when the outside air temps are hot, the entire system under the cowl of a Sonex or Onex is pretty stressed. The installation is tight, and heat tends to build up over time. It's a torture test to fly the plane for an hour on a hot day, then park the plane in the sun for an hour, then fire up and go fly again. The heat from the flight and the baking in the sun heat-soaks everything. Those conditions can be a challenge for even the best installations.
The methods to resist these harsh conditions is a menu of options. You can use a few of these techniques and get some benefit, and a few might be enough to keep the engine performing well in your typical conditions. But, you might need more in the harshest of conditions. You'll just have to experiment to see.
Insulating the fuel system is a great first step to keep the heat out, but if that doesn't work, there are a few other things to try. You can install heat shield/heat deflectors between the hot exhaust pipes and your carb/fuel lines, you can use header wrap on the exhaust to keep the heat inside the pipes and going out the tailpipe, and you can supply the carb body with fresh outside (cold) air. Fresh air to the carb can be a simple as some cool baffle air routed to blow on the carb, or as complicated as an enclosed filter box supplied exclusively with cold outside air that is then routed to the carb. Using either approach will certainly help.
The carb has a pretty good chunk of metal that can absorb a good deal of heat. This means that it will take time to thoroughly heat soak, and it will take time to cool back down again. Keeping the heat out in the first place is a good preventive measure. From my own experiments, I concluded (my thoughts only here...) that my AeroVee just seemed happier and smoother with cool air intake, and that it was worth the effort to install. However, my Jabiru has run ok without cool air largely because it is always flying faster and working less-hard to do so, so the heat soak under the cowl just isn't occurring. Cold air would certainly give me even more margin, but it just hasn't been an issue for me (not to say it couldn't, or it wouldn't for someone else).
Now to the specifics.
BenCharvet wrote:At this point for some reason the electric starter would not operate and I pushed it back to my hangar. After sitting for 20 minutes or so the electric starter worked (I could hear the solenoid clicking even when the starter didn't work), and engine started and ran normally.
This certainly seems heat-soak related. Maybe the starter is binding up internally when hot and expanded, but this goes away when cool. You could try two things. If the starter doesn't turn when hot, determine how easy/hard it is to turn the engine by hand using the prop. If the engine is really tight, this could be a clue. Second, you could put a volt meter on the starter and see what the voltage is at the starter terminal before and during a start attempt. A jammed starter should be pulling a lot of current to try to turn it, and you'd see some voltage sag. Some test data might shed some light.
BenCharvet wrote:I let it idle at around 1000-1100 rpm and tried messing with the mixture control, and it didn't seem to have much effect. I could pull the mixture within 3/8 inch of shutoff, and it still idled nicely, with the same effect at full rich.
It sounds like the mixture is pretty rich at idle rpm setting. Being rich at idle will allow you to lean quite a lot before the engine stumbles. It's common at idle to pull the mixture knob out halfway without any real indication of leaning, then pull some more and it starts to actually lean out, then continue to lean and it runs better and better until you finally go too lean and it quits (all within the last little bit of knob movement). It's just they way it is with the low fuel demands of the engine at idle.
BenCharvet wrote:It had a brief lag on acceleration, but a normal takeoff
Rapid throttle movement on takeoff will commonly cause a brief lag in acceleration. The slide is quickly moved to full open, then the airflow to the engine increases all at once but the fuel flow hasn't quite caught up yet (the fuel droplets have a bit of inertia and don't speed up for a fraction of a second). This causes a temporary lean condition that goes away almost immediately. Slow movements will prevent this. This dynamic is why carbs often have accelerator pumps.
BenCharvet wrote:30 minutes later I hit the Aerocarb with an infrared thermometer and it was still at 135F.
Sounds like the body is retaining a lot of heat. I think you'd benefit with some cool air directed on the carb itself.
BenCharvet wrote:Has anyone made a deflector to direct that heat down and out and away from the Aerocarb/Aeroinjector?
Although I can't recall anyone mentioning an oil cooler heat deflector, it could help. If the air exiting the cooler is bathing the carb body in warm air and heat soaking it, deflecting that air to the outlet and not onto the carb body should help. What are your typical oil temps? The hotter the oil temps the hotter this discharge air will be.
I think you're doing all the right things and on the right track. Keep at it and I think you'll get this iron out. If you have any pictures of the area and your engine installation that might help generate some additional thoughts or ideas as well.
Jeff