$132 for a timer in a 10 year old dryer. My advice, not worth it, even if repairing yourself and saving additional labor costs. This is about half the cost of a nice brand new dryer that you'll hopefully get another 10 years out of. Most appliances have a life expectancy of 10 years, you're there with this dryer.
If a new dryer isn't in your immediate budget I'd just continue using this one as is until you can afford a new one. Set a $2.00 kitchen timer up to remind you when 60 minutes has passed and its time to take the clothes out. | 
Dryer timer broken dries until turned off 
