I have many times in the past temp banned a person for 24 hours. I send them an email, can't use PM since I banned them, telling them I banned them for 24 hours and the reason why. I tell them they are more than welcome when the ban is over.
I will either get a reply with a whole bunch of expletives and some such other rant. Or the person won't reply at all. Will let the ban expire and come back and apologize for their actions and will explain what sent them over the edge.
I have never lost a member after a temp ban. Some stamp their feet and throw a fit. Most take it and come back better citizens.
As far as deleting the posts that lead to the ban I don't delete them. A thread with deleted posts reads like nonsense because integral parts of the thread were removed. I also like to let them be so the offender can see what they did. They could have been impaired.
This is a great take and almost exactly what I have myself done in the past too. I always used to instruct my moderators to issue very short (sometimes as short as 1-2 hours) bans if they felt a situation was escalating (this sometimes happened during football matches when our forum was most active) and this generally worked well and allowed people to cool down before doing/saying something that could've potentially needed a much more serious punishment.
Usually in these situations a simple 1 hour ban with the reason "Cool down" would be sufficient for the person to chill out and come back an hour or two later with a clear head. Sometimes they'd apologise, sometimes they wouldn't, and that was OK by me. It was quite rare for somebody to come back ranting or continuing their previous course of conduct however, and in those cases further action would be taken sometimes needing a slightly longer ban of a few days. But those were rare times for a forum of thousands of members.