I need your MODEL number. You've given me the serial number and the type of dryer. I need the model number in order to cross reference. If this is a Kenmore, the model number should start with "110." followed by about 8 numbers. I apologize for requests for repeated information, but I cannot verify your information without it.
Also, I'm a bit miffed about the symptoms you describe. You said the dryer is running, but doesn't heat. Is that correct? If so, the following link will give you some insight on WHAT components can cause a no heat problem:
Most dryer no heat problems are caused by improper air flow due to lack of proper maintenance. It is very important to keep the exhaust vents free of lint accumulations, rodent infestations, kinks and bends. Simply cleaning the lint trap is not enough. You have to inspect the vent ducting to ensure it is free of obstructions. The rule of thumb when it comes to ventilation is: the SHORTER and STRAIGHTER the exhaust vent, the BETTER. Every bend, kink or sag can cause potential choke points for lint to accumulate. It also creates resistance against the blower motor and forces it to work harder. This will actually cause the dryer to OVERHEAT to the point of failure. It is also recommended that you use the metal semi-rigid type ducting instead of plastic. It is more heat resistant, resists rodents chewing through it (mice love lint for nesting), and resists crushing.
More commonly, the thermal cut-out (also known as a thermister on some dryer models) will blow as it is designed to do. Once this component goes bad, it must be replaced. The reason I mention all these preventive measures is because most people simply do not know, and if you simply replace bad components and don't verify the ventilation, you may have to replace the same components again - real soon. Also, leaving a dryer with dirty ventilation creates a potential fire hazard.
As far as the timer is concerned, this may just be a symptom of your no heat problem. A lot depends on how the dryer is wired. I think we need first need to resolve the no heat problem, before assuming a timer problem. Please let me know some more information about your dryer, so I may give you a more definite solution. I hope that I have been of some help so far.