In a saucepan, brown the beef or turkey with water on medium-high heat. Lower heat and add chili seasoning mix. Simmer, uncovered, for 20 minutes, stirring occasionally.
Add hot dogs to a saucepan of boiling water and simmer, covered, for 5 minutes. Remove from heat. (My note: Alternatively, you can grill the hot dogs.)
Fill buns with hot dogs. Top with shredded cheddar cheese.