Before you start adjusting the PvF, make sure all other things are right:
Make sure all parameters are speaking the same language. F/C, type K/J/RTD, etc. Make sure the TC is the type selected. Make sure everything is connected to the proper places on the terminal board on the PID.
Make sure the devices used have the proper range. Many controllers, TCs, and readouts have set ranges. There is no point in using a readout that maxes at 1000 for a HT oven. Same for TCs - Don't use a 600F max TC for controlling your forge. Generally, the heavier the wire size in a TC, the better it will work and last. Use 8-10 gauge TCs for ovens and forges. Use a TC sheath for a forge. Don't expect good results by pushing a device to its limits. I use 75% of max rating as the working upper range. Your most accurate results will be using a device in its mid range.
Most knifemaker TCs are type K, J, and RTD pt-100. There are many other types, but these three are what we will see 99% of the time.
Type K and J Tcs use two slightly different alloys in each wire, and the junction causes a temperature variable voltage output. All wiring in the cu-ircuit needs to be done in the same alloy as the lead it is connected to. Using speaker wire or lamp cord to connect a TC will cause an error in the reading.
RDTs (Resistance Temperature Detector) are normally lower temp devices. They are a very accurate variable resistor that puts out a resistance change relevant to the temperature of the device instead of a voltage change like type K/J TCs. Platinum is used because of its resistance properties ( pt-100). Many of the issues with type K/J TCs are eliminated by RTD. Observe the lead color code in connection, and all procedures to prevent resistance issues in connections and extension wiring. The main caveat is to avoid adding any resistance to the circuit. The RTD has three wires to connect. It has to go to an RTD location on the PID. If the PID has TC terminals as well as RTD or PT-100 terminals, use the RTD ones. If the PID has only one TC spot, it will have two + and two - terminals. There will be a resistor image that represents the RTD and how it connects. The wires are usually one red and two black (or two white). The red wire is called lead "A", and goes to the positive side RTD connection. There are usually two of these terminals, because some RTDs have four wires ( two A and two B). If using only one red "A" wire, jumper the two terminals together. On a PID I looked at these terminals were #10 and #11. Some PIDs have these terminals internally or externally jumpered already. The two black (or white) wires are called leads "B", and go to the two negative terminals ( sometimes labeled -). On the PID I looked at, these were terminals #12 and #13. It does not matter which black wire goes to which of these terminals.
Make sure all polarity is observed ... Repeat - Make sure all polarity is observed! In a TC circuit everything is polarized.
On type K or J TCs, use the appropriate type TC connector wires ( often designated EXK, EXJ, etc.). It usually comes as a two strand cable. Observe the wire polarity ( yes, the wires are polarized!). Use a TC connecter terminal to connect the TC wires and TC, and type K/J plug/socket for the other end.
On an RTD TC (pt-100), the connecting wires from the RTD to the PID need to be low impedance and the exact same length. All joints should be hard wired on a terminal board with cleaned wires. Avoid twist connections, plugs, sockets, etc. Again, observe proper wiring connections to minimize resistance. The best wire to use is called EXGG three conductor. It is a high temp glass coated three wire RTD cable.
Run the PID for at least an hour to allow it to "learn". You can switch the logic mode in some PIDs to make them more accurate ( fuzzy logic).
If all else fails, then adjust the PvF. Use known temps to calibrate. Boiling water (212F) and ice slush (+32F)are exact references for out purposes. The boiling point lowers by roughly 2 degrees per 1000 feet of altitude. If you live at 5000 feet, water boils at about 202F. The freezing point also rises as altitude increases, but the difference is small, so just use +32F or 0C for an ice bath.