Soldering iron thermocouple measurement HELP
Imprecision in those voltage dividers R1/R3 vs R4/R5 - say, 1% of 24V  = 240mV - will completely swamp the voltage you are trying to measure - say 200C * 4 microvolts/C = 0.8 mV.

Either re-arrange the power circuit to use a high side switch (PMOS for simplicity) allowing the soldering tip to connect to GND, eliminating all that common mode voltage 

Or look into "in-amps" (Instrumentation amplifiers) often used with a current shunt for "high side current sensing" (but with the tip in place of the shunt). These are designed to measure small signals in the presence of large common mode voltages.

I'm not going to feed more details on either approach, part recommendations etc. Either can be made to work so I'm not going to choose : however I suspect high side power switching is probably slightly easier. 

But ensure the input and output voltages are within your opamp's working range. Getting an LM324 working close to its -V supply rail is possible but tricky (pay attention to input offset voltages and output drive capability)