G: TL;DR:
You're describing a common but frustrating issue—severe iPhone overheating and slowdown when connected via USB to your Audi Q3's infotainment system. It's most likely a combination of Apple CarPlay power draw, data sync attempts, and overheating under poor thermal conditions. The Audi infotainment system may be triggering it, but the iPhone 12 has known thermal throttling behaviors that worsen the situation. It’s not just your setup, but it’s not universal either.

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Likely Culprit: CarPlay USB Overload + Thermal Bottleneck

1. CarPlay is a resource hog – When connected, your iPhone:
   • Pushes real-time video output to the car screen.
   • Streams audio and location data constantly.
   • May sync or reindex music/photos if allowed.
   • Charges at the same time (generating heat).
2. iPhone 12 thermal management is aggressive – It throttles CPU, disables radios, and dims the screen when overheated. Its A14 chip also tends to run hot during mixed workloads (like CarPlay + GPS + streaming).
3. Audi’s USB port may overheat the phone – Some factory systems (including Audi) have been reported to overdrive power or fail to properly negotiate USB PD (Power Delivery), especially when used with high-draw accessories or low-quality cables.

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Known Reports

• Audi Q3 (especially 2021–2022 models): Several user reports (on Reddit, AudiWorld, MacRumors) cite similar symptoms: phone overheating, stuttering CarPlay, phone performance nosediving.
• iPhone 12: Documented complaints of heat issues under moderate-to-heavy workloads, exacerbated by charging and GPS use.
• Apple forums: Multiple threads discuss iPhones “cooking themselves” when left plugged into certain cars, even with airflow on.

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Diagnostic Steps

Try these, one by one:

1. Use a high-quality, MFi-certified cable (some cheap ones amplify overheating).
2. Turn off Background App Refresh and disable music sync if iTunes or Apple Music is auto-launching.
3. Set the phone to Airplane Mode, then plug it in—if heat doesn’t spike, it’s likely a network/data overload issue.
4. Try wireless CarPlay (if your Q3 supports it) – sometimes it’s less resource-intensive overall.
5. Cool the cabin and aim an A/C vent directly at the phone while connected (practical test of thermal bottleneck).
6. Use a USB power-only adapter (blocks data, only charges) to confirm if the issue is data negotiation, not power.

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Long-Term Fixes (if confirmed)

• Firmware update for the MMI system – check with Audi dealer.
• Battery health check on the iPhone – overheating may be a sign of degraded battery or internal sensor issue.
• Switch to wireless mount with MagSafe + Bluetooth audio only if CarPlay is too unstable.

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Unlikely But Not Ruled Out

• Failing USB controller on iPhone.
• Misconfigured device profile in the car’s system (try forgetting/deleting the iPhone and reconnecting fresh).
• iOS bug (update to latest, or test with a beta/public RC if you're inclined).

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Let me know if you want to isolate the bottleneck with a debug checklist (e.g. CPU monitoring, thermal throttling readout, or background process check while plugged in).