Here are your parts
Replacement parts for WHIRLPOOL REX3514RQ0 29"electric Dryer | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%208528187.pdf

Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
[COLOR="Red"]Be careful as 240 volts is lethal !!! [/COLOR]

Next check the heater itself. Should be about 10 ohms.
If OK
Check the heater's thermal fuse (Item 6 in Section 3)
If it is blown you have to find out what caused it to go.
Note: that sometimes they do just blow on their own but changing it without checking other things is a gamble.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it.

If the above is OK then you will also have to replace the hi-limit as it should have regulated the temperature so the fuse did not blow.

You still have to find out why it blew.
Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut).

If the heater, high-limit and thermal fuse are OK check the cycling thermostat.

After that all that is left is timer contacts (switch 2) or the centrifugal switch or the motor or a bad wire.

I hope I did not overload you with info but I am off to the lake either today or tomorrow so will not be available.