Your power supply is 9V and your voltage divider produces 660mV. Then if the lower resistor is a 1/4W one it will burn if its current is 0.25W/0.66V= 379mA or more and if its value is 0.66V/379mA= 1.74 ohms or less.
The upper resistor will have 9V - 0.66V= 8.34V across it and its heating is 8.34V x 379mA= 3.16W. Its value is 8.34V/379mA= 22 ohms.
Why are your resistor values so low causing the current and heating to be so high?? Use a 1.74k resistor for the lower one and a 22k resistor for the upper one and they will stay cold.