I think I broke the temperature controller on my very old
Kenmore fridge and I know there are no replacement parts.

I broke it by turning it to far to fast.

Is it worth trying to repair without a schematic or should
I just hot wire it on and use an external controller?

Dick

They make "temporary thermostats" for the repair trade, I used one the
entire time I had one of my fridges, probably 10 years.