CLIMATIC HEATING CURVE CONTROL

Hi, I need to realize a climatic control using logo. The heating curve is the relationship between the heating system supply temperature and the outside air temperature. The heating curve determines to which temperature the heating system have to heat the water at a given outdoor temperature. 

I have all the necessary temperatures measured by PT100 and logo RTD module. 

INPUT: external temp T1 -  I have also the inside building temperature T2 that I'm studying to integrate later in the project.

OUTPUT: output heating water temp T3

The curve can be approximated to a linear one, but I would like to use a function for continuous values and not manually set some step values of the curve. I found online an interesting sample that used a pid controller to set the heating temperature implementation from 0% to 100% based on the external temperature. But after test it, seem to me that not work because in some conditions not work the regulation. I attach it.

Any idea and help?