MT3608 gets very hot only handle 1A
I have the identical board. I connected it to a power supply set to 4.1V, adjusted the booster output to 5.60V and connected a 5.6&ohm; 10W resistor. The output stayed solid at 5.60V while the input current rose to 1.56A. After 6 minutes the chip temperature was stable at 39&deg;C according to my infrared thermometer, 23&deg;C above ambient. The inductor was 41&deg;C, the diode was 42&deg;C, and the load resistor was 112&deg;C!

4.1V * 1.56A = 6.4W input power, so the conversion efficiency was 5.6W / 6.4W = 87.5%.

So this board should do what you are asking of it no problem. However if the input voltage drops the current will have to increase to get the required power, and efficiency may suffer. At 3.7V my unit drew 1.8A and its efficiency dropped to 84%. 

At these relatively low voltages and high currents, any losses in wiring or connectors can make things worse. I used thick wires and heavy duty connectors, and measured voltages directly at the board terminals. I also put 22uF capacitors across the input and output to help reduce voltage ripple.    

Before putting the blame on your board you should consider two things:-


Boosting to higher voltage requires more power for the same output current, and therefore higher input current. Higher current causes greater voltage drop in wiring and connectors (as well as inside the booster itself) making its job harder.
When input voltage drops the chip draws more current to compensate, but this could cause the input voltage to drop even more. If the power source is too weak to deliver the required power then the booster will continue trying to draw more current until maxed out.


18650 Li-ion cells have typical 'knee' voltage at end of discharge of ~3.4V (it might start at 4.1V, but it won't stay there for long). To get maximum usable capacity out of your battery the booster must be able to work down to this voltage, and you need to keep input losses down with short wiring and low-loss connections. 

The MT3608 datasheet only shows output current up to 1A at 5V, and you may need a similar boost ratio as the 3V to 5V curve shown (where efficiency is heading downhill fast at 1A). Therefore, despite being rated for 2A, under these conditions I think 1A is a more realistic maximum.