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The issue is likely a bad electric heating element (or maybe a bad temperature limit switch) - The repair itself isn't all that technical but it can be somewhat complicated because you have to pretty significantly disassemble the dryer to get to the heating elements - It's hard to estimate a cost - A replacement heating element can run anywhere between $30 and $75 depending on the model, and it's probably a 2 hour job once the technician has the proper parts. Labor rates vary so much in different locations.
You can search by model number on a number of appliance parts websites - one of my favorites is Sears Parts Direct. Sears also has Sears Home Services, who should be very qualified to repair the Whirlpool dryer.
Also, most appliance repair contractors will tell you that a 10+ year old appliance should be replaced. A clothes dryer has very few moving parts - A belt drive motor that turns the drum, the heating element kit, and the controls, most of which were very uncomplicated on older appliances. As long as the element is the only real issue I'd insist on the repairs.