Assuming this is a petrol engine (you didn't say), the turbo is cooled both by engine coolant running through a water jacket and by engine oil running through the turbo bearings. But a turbo can still become extremely hot after racing, after running at constant speed on a motorway, after a long ascent, or after towing and if you switch off immediately the oil in the turbo bearing oil feed and oil return pipes and in the turbo itself can carbonise, contaminating the engine oil and restricting the oil flow through the turbo bearing. So best to let it idle for a minute or two in these circumstances. If the engine has stop/start and it switches off automatically, no need to worry. But if it continues to run, do not switch off. No need to worry about any of this after short, suburban journeys. The turbo won't get too hot.