Your drawing is about what you want. A few years ago I sent some temperature transmitters to another forum member. They look pretty much like what you have:
View attachment 87398
There are a few versions but they all do about the same thing. They convert a signal from a thermocouple, RTD or other temperature sensing device to a current which is generally 4 to 20 mA. Below is an image of what a basic setup would look like:
View attachment 87399
Resistor R1 in this illustration is what I was mentioning earlier. In this case the 4 to 20 mA in the loop is converted to a voltage drop across the resistor.
I have a rough idea of what you have for this "alarm panel". They are called alarm panels, supervisory panels and a host of other names. Most use input cards so you can set the device up for various inputs. Doing what you want to do won't be easy. I don't know of an easy way to get from the 4 to 20 mA current loop you have to a resistance. Depending on how this alarm panel input is configured you may be able to run directly in from your PRT probe? Then write the software routine so the panel can derive a temperature from the resistance input. Unfortunately there is no simple magic box. I know cards for these panels can get expensive. It sounds like when everything was purchased there was some lack of communication.
I like Jim's approach above.
Ron