Heat the grill.

Mix the mustard, ketchup and sauerkraut in a small bowl.

Slit the hot dogs lengthwise, forming a deep pocket end to end in each one. Fill the pockets halfway with the sauerkraut mixture. Put a stick of cheese in the center of each and top with the remaining sauerkraut mixture. Wrap a bacon slice around each hot dog to hold it together, and secure the ends of each bacon strip with wooden toothpicks.

Put the grill screen on the grill and coat it with oil. Wait a minute or two, until the surface is hot. Grill the hot dogs until the bacon is cooked through and the hot dogs are browned on all sides, about 2 minutes per side.

To toast the buns, put them cut-sides down directly over the fire for the last minute of cooking. Serve the hot dogs on the buns.