You really should let it cool down if you want things to last. Cooked oil in a hot turbo turns to carbon grit, not well known for it's lube qualities.
Many pyros aren't accurate at the lower end of their range what you're seeing as 350 could very well be 300. Take your truck for a non-towing short drive and let it idle for two minutes to see where your particular gauge reads for safe shut down. The pyro in my 3500 would never get down to 300 idling all day.