Kenmore elite dryer runs but doesn't heat. What should I do first?

Gas or electric?

How old is it? If it has had a lot of use since you bought it it probably is stopped up with dirt which burned out a safety. You have to disassemble it and clean it out very well by scraping and washing out all parts except motor, which you vacuum out. All parts that handle air must be cleaned, including the blower fan and all air ducts and element housing. Then you have to use a meter to find blown safety and replace it. It's all easy to do and will take 2 to 4 hours. Be sure to replace belt, as well. DrTom4444