How do you handle a toddler tantrum in public without losing your temper?

The first thing that helps is knowing that public tantrums are developmentally normal and not evidence of poor parenting — a two-year-old has adult-sized feelings and almost no capacity to regulate them. What works in the moment: get down to their level, keep your voice low rather than matching their volume, name what they are feeling, and move somewhere quieter if you can. Do not try to reason mid-tantrum, since the part of the brain you are appealing to is offline. Deal with the audience by ignoring them; most parents watching have been there.