Hello DickandKendra! You've already done the difficult part, which was to find and locate the faulty thermal fuse (switch). Now you should be able to get a new one and replace it pretty easily, just be sure to unplug the dryer before you start taking it apart, etc., but you already knew that.
If you need to determine what the replacement part number is for your particular dryer is, please go to www.searspartsdirect.com
, since you didn't post your model number, I can't provide you with the part number directly. No problem, you can find it by entering in your Dryer model number and then click on the links that show up to locate the thermal switch. There will also be a line drawing of your Dryer, so you can search by the picture, etc.
I think that possibly that the dryer motor has failed and that is why the thermal fuse went out, but you should probably just replace the fuse 1st to see if that's the only issue. When you replace the fuse, just run a drying cycle without heat, (only air fluff, etc.) so you can see if the motor starts and runs. If it does, then the thermal fuse was the problem, if the motor doesn't run, you've got a faulty motor and it'll need replacement.
Of course, if you're comfortable with doing a temporary bypass of the thermal fuse, you can also check the motor function before you order and replace the thermal fuse, to determine if the motor is faulty. The temporary bypass is ONLY to be used to diagnois if the motor is good or bad - DO NOT leave the thermal fuse bypassed, as it's purpose is to prevent a dangerous overheating problem that can cause a fire. This is only to be done as a temporary measure to determine what caused the thermal fuse to blow!
This will allow you to determine if you want to spend the money and time needed to replace the motor and thermal fuse, or weigh those costs against purchasing a new dryer - your option. However, if the dryer is still in good condition, it will cost much less than buying a new one, even with the cost of these couple of parts.
I hope you find this Very Helpful and best regards!