Modbus RTU Implementation to Automate Temperature through PIC Microcontroller
RS-232 are point to point connection this meant you can only connect the wires to a master and a slave as apposed to RS-485 which can be multydrop. 

modbus is a fairly easy to work with it just reading and writing to registers. 
take a look at this link these guys give you a lot of information.

At the start of your question you mention PLC is that correct or men to be PIC as a lot of PLC have built in modbus and with easy to work with library. PLC also come industrial ready and tested and do not require a PC. A PLC would be a better solution then a PIC if your not wanting to make a PCB and wanting a reliable controller.

Even better remove the Watlow F4 temperature controller and use the PLC with a HMI to do it all. if the wiring is simple. wire the temp sensor to the PLC input and the Heater on/off or/and up/down to the output.

If you still want to use a mico i would recommend using arduino to do this as it easier to get started, the code is simpler to work with and there is lots of examples. this guy id using RS-485 but it will give you an idea if how it done link.