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Turbo beanies trap the heat, when shutting the engine down the car should idle for a set period of time to let the cooler water and oil to pass through the turbo. This stops the oil and water almost boiling inside your turbo killing your bearings.
A turbo timer does this trick automatically.
You mention heat soak. ( Remembering that turbos beanies only block radiant heat, not conductive ) Best described as heat transferring from the exhaust side of the turbo to the compressor side of the turbo heating your air that's being fed into your engine. Everyone has their theory on how much it does heat the compresser core up.
A intercooler will eliminate that, as the "warm" air that's now being heated up by the turbo passes through the intercooler.
The plus side to a turbo beanie is it traps that heat into the turbo, and we all know heat= energy. Some even go as far as saying that the turbo will spool faster. I don't think the difference would be noticeable, but im no expert.