Similar to apples and bananas. I will call the parents to give them a heads up - basically a warning to put your day in order since you may be needing to leave early and/or you might want to make a doctor's appointment for your child for later in the day.
My kids always had very high fevers no matter what and while I used to get very upset my doctor always said he was more concerned about a child with a low fever but was lethargic than a child with a high fever that was trying to go about with their day and the main concern was to maintain hydration.
Yes the child is sick and might even be contagious but they have been contagious all morning so letting them rest on the couch for a few hours isn't going to change the fact the others have been exposed. As well not all infections are as contagious as you would think so yes there may be an ear infection but they won't necessarily spread it. And yes viral infections are also contagious but you can't do anything for them other than make child comfortable till it runs its course.
I use common sense more than rigid standards of when to call a parent to send a child home. It has to do with the health history of the child and how old they are such as a baby that can be put aside in a playpen or gated area or exersaucer or given a longer naptime is easier to manage than the child that is coughing and sneezing all over their friends and the toys because they don't know any better.