Dc heater that will/should blow hot air
Let's roll this up from the bottom:


  And finally, is it a good idea?


Firstly: at "around 16 W", your heating produces as much energy as let's say half a tealight. In other words, as long as the room you're heating isn't very small, you probably won't easily notice you're heating it.

So, and this is intuitively not very surprising, with a bit of wire fed from a 20 Ah battery running at 3.7 V, you don't get your room really warm.

Let math persuade you:

Air has a specific heat capacity of pretty much \$1 \frac{\text{J}}{\text{gK}}\$, i.e. it takes one Joule (\$=1\,\text{Ws}\$) to heat up a gram of air by one degree Kelvin/Celsius. Now, together with the density of air at sea level at roughly room temperature, that means that you get a volumetric heat capacity of air of roughly \$1.3\cdot10^{3}\frac{\text{J}}{\text{m}^3\text{K}}\$, or: to heat up a cubic meter of air by one Kelvin, you need \$1.3\,\text{kJ}=1.3\,\text{kWs}\$.

Let's say your fan gives you (and this is a wild guess based on a 11W fan I found online) \$80\frac{\text{m}^3}{\text{h}} =\frac{80}{3600}\frac{\text{m}^3}{\text{s}} =0.022\frac{\text m^3}{\text s}\$. 

You have 16 Ws = 16 J that you put into this per second. So the air coming out of your heater is warmer by 

$$\frac{16\,\text{Ws}}{2.2\cdot 10^{-2}\text m^3 \,\cdot\,1.3\cdot10^{3}\frac{\text{J}}{\text{m}^3\text{K}}} = \frac{16}{22\cdot 1.3}\text{K}\approx 0.6\,\text{K}
$$

i.e. barely, if at all, noticable.


  how much power is good enough for that purpose so batteries can last for some time and dont blast on my face?


Seriously, there's no magic. Either you drain your batteries fast, or you won't get warm air. You can't have both – conservation of Energy is among the things that this universe (magroscopically) depends on.

@marcelm made an excellent comment:

Your hair dryer has 1500 W. Your heating has 16 W. That is but 1% of that. How warm do you think 1% of the heat of a hair dryer is? Not that warm. The wind will probably make your face feel colder, not warmer.