I'm assuming this is electric.
Most Kenmore's are the same as a whirlpool. First check to see that both legs of the power are hot (220v) A dryer (as well as a range) will run on 110v, If you only have 110 power, check to see if a house fuse, or breaker is triped.
It has one heating element. If you can take the back off (unplugged machine!!!) its a metal cartridge to the right towards the bottom.
unplug the heating element and check for resistance. There should be a fair amount Cant ember the value but less than infinity. If it reads good you will see a disk with a screw in each side, mounted near the element (high limit) test it also the same as the. There should also be 1 more of these thermo disks for each heat setting (not counting the air fluff) test them as well.
connected to the I limit with a Short wire there is a therm fuse, check it also, same as you did with the heater, if its blown, thin your high limit is also blown (stuck on) this is a safety that will blow to keep your coil from getting to hot, and starting a fire if the high limit doesn't turn off.
use this advice with caution. don't get electrocuted!
almost forgot, if the dryer works on one heat setting, and not another, its almost always a thermo disk, could be the selector switch too, but that's rare.