David,
What are the fitting sizes in the rad.? If you are talking about #6 fittings or so the the pressure drop across internal Radiator cooler will be high. This P drop will be too high and defeat the #12 feed= return line size. Adding 220 to 240 degree
oil to an already taxed coolant system may not help on a race toy. They do it on factory cars but have all engineering paramiters to design a give and take system.
Adding a DPDT SW = double pole double throw switch with 2 sensors lets you read 2 points but temp at engine is more useful.