Does ATX power supply really need its cooling fan when drawing only 3A at the +12V rail? I know that the fan is mandatory when it's running a computer that draws 200 Watts and above but is the fan required if the load is just 36W?
A fan is necessary to maintain the components within their operating temperature range. That's all. So if you have a supply with a super efficient design, you won't need any fan, even at 200 watts. If you have a supply with a super inefficient design, you'll need one running even at 5W. Besides, the need for active cooling also depends on the ambient temperature.
So, your question, as formulated, really isn't answerable, except if you provide the complete datasheet of the supply and indicate in which condition you'll be running it. And even then, I'm not sure the datasheet will provide enough details to be definitive about whether you'll need the fan or not.
But I guess the underlying question is "can I use an existing ATX supply, remove the fan, and hope it will still run properly if I draw only 36W?".
The definitive answer is likely no. At least, I wouldn't do it. ATX supplies are certainly not designed to be very efficient at low load. I'm pretty sure they are optimized for much higher loads, and 36W could still be stressful enough for a few components without active cooling when running for a long time, or if the ambient temperature is high.
Now, many recent ATX supplies have automatic thermal control of the supply fans. So if your supply has this feature and the fan is already running at 36W, you'll be absolutely sure you can't do without it.
Anyway, the right solution to get a 36W supply with passive cooling is to buy one. There are many to choose from, at reasonable prices, they will be designed to be efficient at this load level, and they will be much smaller.