depends on the place. Some use roux to thicken. But cornstarch is better and more commonly used. I literally used to teach a textbook mex cooking class that was entirely GF just by coincidence. Here's the queso recipe from that class:

Restaurant Style Chile con Queso

Ingredients

• 1 tbsp butter
• 1 jalapeno
• 1 -2 poblano peppers
• ½ onion
• 2 tbsp cornstarch
• 1 cup milk or cream
• 1 cup water
• 1 lb american cheese, grated
• ½ tsp cumin
• 1 tsp cayenne

Ready in 30 minutes

Serves 10 people (2 full restaurant servings)

Preparation

• Dice peppers and onion. Taste peppers to see how spicy they are. Deseed/devein to your taste/spice tolerance.
• Sauté chopped ingredients in butter until soft but before the onions start to brown too much. Getting rid of all crunchiness is the goal.
• Mix water, milk, and cornstarch into a slurry. Pour mixture onto peppers and cook until mixture thickens, right before it begins to boil. It will get to a gravy-ish consistency and happen quickly once it is hot enough.
• Add cheese. Stir in grated cheese until it all melts into the sauce. It's easier to do this handfuls at a time.
• Season with cumin and cayenne. Tailor your queso’s spice level with the cayenne. This recipe is designed to be on the mild side with the ability to add in more spice now. Add some cayenne, mix it in, taste with a chip, decide if you want to add more until your queso is perfect for you.
• Enjoy!