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Parts for Roper RED4100SQ0 Dryer - AppliancePartsPros.com

See the attachment for the tech sheet.

This unit does not use a moisture sensor.

Below is my usual blurb on replacing a blown thermal cutoff.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 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 so the thermal cut-off blows.

The hi-limit should have regulated the temperature so the fuse did not blow, that is why there is a new one with the thermal cut-off..
Note: That unless there is another problem in the unit the hi-limit should never have to open. It is just a safety device with the fuse being a backup safety device.

Just in case it is not a grounded element.
With all the below the high limit will also have to be replaced.
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)

So I just tested the cycling thermostat and that was one of the first parts because it came with the high limit fuse that originally started this fiasco.
I think you have your parts confused.
The kit you received would have been the thermal cutoff (high limit fuse) and the hi-limit thermostat.
The cycling thermostat is mounted on the blower assembly.

[COLOR="Blue"]The thermostat is showing resistance with the dryer off the version in my dryer only had 2 wires.[/COLOR]
Is this 0 ohms, it should be.

[COLOR="Blue"]Is it possible this thermostat has s higher temperature rating that the previous[/COLOR]
You are looking at the wrong part.
The temperatures should be:
Thermal cut-off 309 degrees
Hi-limit thermostat 250
Cycling thermostat 135 to 155 adjustable
Thermal fuse I do not know.

[COLOR="Blue"]also there is no resistance on the heating element housing like someone else mentioned. [/COLOR]
I am assuming that this is the test for checking if a heating element is grounded.

[COLOR="Blue"]how do I get the thing out? There are no screws its just attached through a metal prong or do I have to replace the coil and the housing?[/COLOR]
The side that is on the heater element is disconnected and then it should then unclip from the little tab on the right side.

You are welcome.

And thanks for getting back to us. Now when others search for a similar problem they will see what actually worked instead of just suggestions about what could be the cause.