It's true that a 10k resistor will heat up more than the 10 ohm resistor if the current is the same. This is because for a given current the heat is proportional to the power dissipated by the resistor, which is in turn proportional to the resistance.
However in your case, the current depends on the resistance, and you need to take that into account.
Start by calculating the current as voltage divided by resistance. Then since the power is the voltage times the current, you end up with power being the voltage squared divided by the resistance. You have the same voltage for either resistor, so the heat is going to be inversely proportional to the resistance.
Since the 10 ohm resistor has 1/1000 the resistance of the 10k resistor, the heat will be 1,000 times greater.
By the way, the current rating of your power supply is the maximum that the power supply can handle and doesn't determine the amount of current that flows