Here is the parts breakdown
Replacement parts for WHIRLPOOL LEQ9558KQ0 | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%208299799.pdf
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I believe this should measure to have continuity, am I on the right trail?[/COLOR]
Yes it should be 0 ohms.

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. I believe richappy (another regular poster on this forum) has done a study on thermostats and found a wide variation of actual trip point and what is specified.

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).