Problem after replacing THERMOSTAT with a MARCONE part

Hope someone can help. I have an 8 year old Kenmore SxS refrigerator that would only start after tapping on the control panel. When I removed the thermostat the contact points looked burned and if I moved the terminals it would start the frig. I figure I found the problem, but the replacement part might have caused another problem. (?)
I replaced the THERMOSTAT with a brand sold by MARCONE, not the Sears EXACT replacement. The difference was the thickness in the long wire that detects the temperature. The new one was considerable thinner!
Now the frig stops, again, and everything in the frig compartment sweats and defrosts.
After reading some of these posts I figure that because of the difference in thickness of the wire detector it has altered the balance or adjustment to the DEFROST TIMER. Is that the cause of my NEW problem? I saw the defrost timer detector right next to the thermostat but it did not look that it had any adjustments on it.
Thanks in advance for any help with this. - Oscar
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