Good. It's every experimenter's responsibility.
Please, if you dont have anything useful to contribute just leave, your "don't do it" comment is not helping me in any way. I was not asking you if i "should" or "should not" do a project, my question was a specific one and u dont offer anything constructive to help me out.
Keep your comments to yourself.
Thank you.
Well, you are not the only person reading this thread. So I'm not just talking to you, I want to make things clear to anyone who stops by here to read.
Bottom line, the thermal time constant of a heater like that is so long, that PWM is completely futile and unnecessary. You could still use a PID with "bang bang" control (although it's not quite the same), it would definitely be more appropriate and much easier for you to achieve.
Bonus, you won't radiate for blocks.
If that isn't constructive, I don't know what is.
Furthermore, I would ask what experimentation you have performed so far? That would give you a better idea of what direction the hardware/software development should go.
Again, consider reply #5.
It has a Vgsth of 2V, so it should be fine, they don't state that it is logic level, but the Vgsth seems to fit.
Tom... 
I've been working with the Temperature Control Lab hardware to develop a PID autotuner. This hardware setup does what the OP proposes, only it's maximum output is 10W. The thermal time constant is 2.9 minutes, so it takes about 15 minutes to reach any new setpoint temperature. It uses 8-bit PWM for output control and the input resolution is limited to 3.1mV per step, which is quite lousy, but ideal for development.
I can't wait to complete the development of the new library, but this time of year is sooo busy with, well, everything. Anyways, take a look at the plot here, where green is the PWM duty and red is the temperature (input). No manual PID tuning was performed.
If you don't want to take good advice, this forum is not the place for you.
You DO NOT NEED PWM for this application.
There's thousands of MOSFET modules out there that could make things easier. Note that you can't really avoid PWM. Direct output control of a MOSFET or relay is techiically a form of PWM at a much lower frequency.
How tightly do you need to control the temperature (± from the setpoint)?
No, you probably want a 40+A rated MOSFET - going close to the limit means the MOSFET will have to be heavily cooled with a massive heatsink.
Say you want a MOSFET that only dissipates 1W for an 8A load. I-squared-R says it should have an on-resistance of 15 milliohms or less, and will only need a small heatsink.
The on-resistance is what you use to determine a device, not the max rated current (which is typically an abs-max thermal limit and always bad news to reach)
@TomGeorge i decided to order both IRF3708 and IRL3705, both available in my country, based on some calculation that i did it they should perform similarly, at least when it comes to how hot they will be during operation. 80°C vs 75°C approximately, so i will just test them both and monitor their temperature and decide which one to keep, although IRL3705 has a bigger headroom on amps and like @MarkT noted better to not push things to the limit.
I will use a heatsink later on, but the thermal tests of the mosfets will be done without one first just to get a clear picture.
@dlloyd The temperature control should ideally never overshoot above the setpoint, it can be lower than the setpoint since that will not be a huge issue (by lower i mean up to 3°C) but should not go above the setpoint since that will probably mean the death of certain bacteria. Just as a remark, the ideal temperature to force this specific bacteria to ferment milk is 46°C, going somewhere between 42°C and 46°C is still gonna work but going above 46°C will start killing things in the long run. So you really want to keep it stable at 46°C for 8 hours to produce a thick and creamy yogurt.
I had a look at your GitHub, i will use your PID code since you specifically state that you try to fight against overshooting temps which is exactly what i am after. Will let you know how it went when my order finally arrives and i can get my hands on it.
Thank you everyone for your suggestions and input.