Codes P0605 & P0700

Bought a 2002 PT Cruiser last summer now have an intermittent problem that developed this winter. When the outside temperature dips down to the lower 40s or lower, the transmission goes into limp mode and CEL comes on w/ the P0605 and P0700 codes. When the outside temperature gets warmer the transmission operates normally and the CEL goes out.

It is my understanding the P0700 is simply saying there is a fault code in the TCM and the P0605 is an internal failure in the TCM itself.

If the failure is in the TCM (P0605) then do I go ahead and replace the TCM or is there something else I should try first?

Also, any idea why the temperature would be the cause of the fault?