Welcome to DC!! The OP wrote of toasted cheese, not toasted cheese sandwiches which is different. He/she didn't mention sandwiching the bread slices together. Apart from the heat issue, certain cheeses don't grill well and all they do is puff up and brown so you may wish to try a different cheese, one that is less processed perhaps.
I think the confusion lies with what the OP called the thread and then said they used a toaster oven to produce the end product, which was not named as grilled or toasted cheese. So, until our OP clarifies, we're just having to guess either way. Plus, sandwich is in the eye of the beholder. One of my favorites is an open-faced roast beef. The poster could, in effect, call their creation an open-faced cheese sandwich.