The MOSFET does not receive heat it generates it when overloaded, not driven properly, not heatsinked adequately and many more. Along with the schematic show a picture of the assemble. Also it appears this is a three phase motor so include a link to that as well. Can you post scope photos of the gate drive on one channel, both fets, and hopefully a current trace.
My guess is that you are getting what is called "shoot through". This happens when both the top and bottom of a pair of FETs are on at the same time for a short time during the process of turning one on and the other off.
This in effect causes a short circuit through the FETs and hence you draw a lot of current and the FETs will generate a lot of heat and so burn out.
The bootstrap caps and diodes are also suspect.
A common 10uF electrolytic smd can can't supply the several Amp gate pulses.
Probably needs to be Tantalum. See the chip's datasheet.
Same for the caps on the 12volt rail (chip).
Diodes must be fast recovery (Schottky). The diagram shows common diode symbols.
A 23 milli Ohm fet has a static dissipation of ~4.5W at 10A. Without the switching losses.
Those heatsinks can maybe dissipate 2W.
Leo..
If you already have a Schottky diode there, then don't replace.
The first schematic shows a common diode. A Schottky has another symbol.
The gate of a fet is like a capacitor. For fast switching of the fets, that capacitance needs to be charged/discharged fast, which the gate driver chip tries to do.
But that energy has to come from somewhere. The supply caps. Stick with the value that the driver datasheet gives you, but use caps with a low ESR (Google that).
Leo..
10 ohm is a more realistic value. 100 ohm sort of defeats the use of a gate driver chip.
A 1N4148 smd diode on top of the 10 ohm resistor could further reduce switching losses.
Google "ir2104 circuit diagram" (images).
The type of cap is more important than it's value.
The 3.3 milliOhm of that fet is much better than 23 milliOhm.
But sort out the gate drive chip parts first.
Leo..
Your help was very helpful.
However, there is one problem.
I understand the concept of ‘ESR’.
However, it is difficult to find the 'ESR' value published in the capacitor datasheet.
2.2uF
Polarized products
By any chance, can you recommend a product number? Or even the manufacturer?
No matter how hard I search, I can't find a capacitor with 'ESR' written on it. I don't know which is better.
You will never find a capacitor with the ESR written on it. It is only on the data sheet you will find this. And if it is not on the data sheet then it must be a bad figure, so reject that one as well.