I've many of my late Father's Kodachromes (all Kodak factory processed) from the 1960's which he used extensively for public and private shows and these still look fine. I'm sure, in normal circumstances, damage in a minute could only be from a faulty projector or over-powered lamp; he used a Leitz Pradovit (which I still have) and slides are barely warm after even 10 minutes projection.
I've scanned the most important ones, but this has been mainly to have a duplicate record, copies for other members of the family or against physical damage rather than any major concerns about projector damage.
And remember that slides were designed mainly for projection.