If you quit going out to lunch with them, they will most likely think you're that arrogant boss. If you quit going out to lunch with them now, I wouldn't expect to pick the practice back up when the permanent replacement arrives. You're just the temp, and your boss let you know that when the term "Suitable Replacement" was used. Don't ruin your working relationship with your coworkers because you've been given a short term assignment.

I've held several managerial positions where I was promoted from within. They always went the best when I let my workers know up front that I was going to have to adhere to the rules or ask for changes where I felt it necessary, not that I ever played fast and loose with the rules anyway, and that I expected them to do the same.

Let them know up front that you will treat everyone fairly and that should now expect you to make managerial decisions whereas you didn't previously. Within that idea convey to everyone that it's Day One as far as you're concerned. If they have a clean slate no one will be freaking out over past offenses that you know about such as calling in sick so they could go to Vegas or whatever. Having said that, let them know that you're not a pushover and if someone has a recurring habit of doing things that are against company policy or other and you didn't previously report it to management, tell them that you expect the behavior to stop.

Unfortunately you're in a tough position because it's not permanent.