Blower motor resistor keeps getting hot and blowing

The problem was the motor. Replace the blower motor and resister and it should be fine.

If the blower motor resistor is experiencing repeated failure, the blower motor is likely drawing too much current. Excess current draw from the blower motor will cause the resistor to burn out. The blower motor in your truck has a resistor block with multiple resistor wires.
Jun 21, 2023

Why Does the Blower Motor Resistor in My Dodge Dakota ...

More here

https://www.google.com/search?q=2004+Dodge+Dakota.+It+keeps+blowing+the+blower+fan+resistor

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a Volvo (must we guess"?) 2010 xc 60???? no air jumper-ed too?
if yes controls bad.
but with all blend door motors dead, air will flow.
there is no blower blocking door/damper ( but Filter)?
no air flows? means what?
hot air?
cold air?
either?
or no ambient air flows. or all.above.?

most cars have at least 3 dampers
MODE (direction)
hot cold, manual control.
recir'/fresh.

case in point, if hot core and AC core are dead
and blower spins you still get ambient cab air flow or fresh.
cab filter clogged up.
I need more facts to know what tests to do.

https://eautorepair.net/Marketing/Default.asp

Possible blower motor is defective pulling excessive amperages causing fuse to blow continuously regardless if its still operable.

blower motor resistor, had the same issue replaced blower motor resistor

I would agree. If you wire it direct the wires should not get hot.
The resistor will get hot under normal conditions because the resistance is how the motor speed is controlled.
So you are probably right the motor is failing.
You could get a new motor and hook it up without installing it to compare.

Check your blower motor resistor connection.Turn switch and fan on then wiggle the resistor pigtail fan should turn on if not replace resistor.These get to hot and usally melt the pigtail and loose their connection.

the resistor is indeed very hot! and you are right it's cool by the blower, that's why most resistors are in the blower case.
the fuse was blown because it's not the right amp rating or the blower may be going bad.
.

IT COULD BE BLOWER MOTOR NOT GROUNDED.YOUR BLOWER MOTOR FUSE AND RELAY COULD BE BAD.MAKE SURE POWER IS GOING TO BLOWER.MOTOR.CHECK TO SEE IF POWER IS GOING TO SWITCH IF SO SWITCH COULD BE BAD.HOT WIRE BLOWER MOTOR USING JUMPER WIRE AND POWER FROM THE BATTERY.IF BLOWER MOTOR WORKS.YOU HAVE FUSE RELAY AND SWITCH PROBLEM.MOST THE TIME WHEN RESISTOR BAD.YOUR BLOWER MOTOR ONLY WORK ONE SPEED SOME TIME.

The blower motor has too high off resistance,this why resistor keeps blowing.

If the blower moter only works on hi speed it is the blower motor resistor that is bad. The blower motor resistor is located under the passenger side of the dash next to the blower motor. It is not necessary to remove the blower motor to change the resistor.