This answer will be related to this one and this one. So rather than diving deep into the abyss, I'll more or less present the information because the person asking has proven himself/herself/itself to know what s/he/it is doing.
Here's the important data from the datasheet
- \$t_{D(ON)} = 7.6\text{ ns}\$ = delay when turning on.
- \$t_{D(OFF)} = 22.2\text{ ns} \$ = delay when turning off.
- \$t_r = 57.6\text{ ns}\$ = rise time for output to go from 10% of VDD to 90% of VDD.
- \$t_f = 16.8\text{ ns}\$ = fall time for output to go from 90% of VDD to 10% of VDD.
If you would ignore the delays and only focus on the rise and fall time, then the maximum PWM you can use is \$\frac{10^9}{57.6+16.8}\approx13 \text{ MHz}\$. So if you would use the PWM at this frequency you would get triangle waves at the output => definitely not wanted. These transitions are when the MOSFET conducts a lot of current and has a lot of voltage across them => a lot of power.
So a good rule of thumb, in my opinion, is that the transitions should only occur about 1% of the total time. The less the percentage, the lower the frequency and the higher the efficiency will be.
So the maximum PWM frequency I would go for would be \$\frac{t_r+t_f}{T}=\frac{1}{100}\rightarrow T = 100(t_r+t_f)=7.44\text{ µs}\$.
\$\frac{1}{7.44\text{ µs}}=134 kHz\$, this is a reasonable max frequency.
The delays won't really affect the switching frequency, they will just skew the PWM in time, which you won't really care about. There are some other delays however, the gate of the MOSFET has a capacitance (not an actual component that you can remove, it's a part of the MOSFET, like your belly button is a part of you). When you are making the gate go high and low, then you are charging/discharging this parasitic capacitor, so this means that the rise time and fall time will be slower because you will be charging/discharging the gate with an MCU that can source and drain like 20-40 mA. So in reality you might want to use 100 kHz instead as your maximum switching frequency. Also the gate resistance will make it even slower, but it will remove the ringing, the price for low/no ringing is slower transition times. And it is a good price to pay. Well worth it. If you want to actually drive it in higher frequencies, like 130 kHz or maybe even 250 kHz, then you will need a MOSFET driver chip.
Either way, so we know that 100 kHz is, in my opinion, the maximum switching frequency. What about the lowest?
"heater is a coil of tungsten (diameter around 5mm) wrapped around a steel tube", this has some mass, I don't know what exactly, but 5 mm is pretty small. I am fairly certain that you can drive things fairly correctly with just 50 Hz PWM. If your heating element had been connected to a lot of thermal mass and used for something less important, then 1 Hz PWM would've sufficed.
But if I were you I would just go as high as high as the MCU will allow, and under 100 kHz and call it a day.
Some comments:
"I'm designing a circuit to control voltage between 2.8 and 4.0 volts using a PWM", are you talking about the average voltage of the PWM? => you will use a duty cycle of \$\frac{2.8}{4.2}=66\%\$ to \$\frac{4.0}{4.2}=95\%\$, if you are, then nothing is weird. Everything is good.
"The load is a resistive heater (0.2 Ohms) between the positive pole of Li-ion battery (4.2v - 40 amp nominal current)", wasn't it 20 amp nominal current?
I presume that your schematic looks something like this right now. Put your mouse over the graph's and look at what elements that light up. The two graph's on the left indicate (in green) the voltage across the elements they are connected to. The right graph (white) indicate the power across the heater. Have a look at the average power across the heater.
"I was taking about the voltage that pass through the heater that will alert its heating temperature.", hmm, I'm still not following, but maybe that doesn't matter. I think I probably don't need to understand it either.
