Say we had a circuit with a cell (with internal resistance)and an external resistor of 10 ohms as shown:
The 10 ohm resistor then increases in temperature, leading to an increase in resistance in this resistor. My thinking was that since the 10 ohm resistor now has a value higher than 10 ohms, more voltage drops across this resistor. Since your emf is constant, less voltage must drop across the internal resistor. Less voltage drop means less resistance. Where is the flaw in my logic?