When I need to reheat hamburger patties I take the hamburger patties and place them in a baking sheet.
Then I preheat the oven to 350 F while preparing the hamburger patties.
After placing the hamburger patties into the baking sheet I place them in the preheated oven and allow the hamburger patties to sit in the oven and heat up for around 10 minutes.
If the hamburger patties that you cooked were frozen then it may take 30 minutes but if you just had the cooked hamburger patties in the refrigerator then heating them up for 10 minutes is usually enough time.
You can also reheat the hamburger patties in a toaster oven or in the microwave for a few minutes.
Or you could use the skillet to reheat the hamburger patties really quick just keep an eye on the hamburger patties so that they do not burn.
I find heating the hamburger patties up in the oven works best for me though.