Just say NO to wire nuts in your transfer switch.
The problem is, the wire nut screw threads cut thru stranded wire when connecting to solid wire; i.e. romex. The tighter you tighten them, the more they cut thru the stranded wire and cause a high current especially when you turn your AC on or other heavy elec. load.
Like others and myself have done, remove the stranded wire from the transfer switch and connect the solid copper wire directly to the lugs on the TS.