Can I put my iPhone in quiet mode only for a limited period of time? When going to the movie or attending to a talk, how can I put my iPhone in quiet mode only for a limited period of time, like one hour?

In particular, it is mostly the case that I will forget to disable the quiet mode when the movie / talk is finished and that I would miss calls or notifications.

I tried this by settings, or asking “Siri”, but the answer was that it is not possible. This would be a great feature.
Source
Your best option is to use Do Not Disturb.

There are multiple new limited-time settings for Do Not Disturb in the Control Center, which automatically turn off after the specified time elapses.

For one hour
Until this evening (or afternoon/morning depending on the time - it's generally a few hours)
Until I leave this location
Until this event ends (if you have a timed event set in your calendar)   A single tap on the icon without selecting an option turns
on Do Not Disturb until you tap it again.