Pinout of / how to charge that certain battery (Lithium-ion, 3.7 V, 2 Cells, parallel, 4400 mAh)
Try usinga TP4056 based Lithium battery charger module with built-in battery protection. They are very cheaply available in bulk on popular shopping websites, and the datasheet has a table of resistor values for programming the charging current (if you can't find a module pre-made for your required charging current, see below). 

The chip handles the charging of the battery completely on its own, with a single 5V power supply (most if not all those modules have a USB socket on them). If the cells are parallelled in side the battery, like in most powerbanks, they're just hardwired together without any balancing means.

Charging a lithium cell is easy, as long as you consider the maximum input current of the battery. If there is no such value available, use the half-C-rule (charging current does not exceed 0.5 times the mAh rating of the battery). 

The battery is first charged with a constant current, until it reaches 4.2 volts. The charger then switches to constant voltage mode, until the charging current has dropped below a threshold value. The TP4056 has all the means to do this on its own, including a "soft start" for charging deeply discharged batteries, starting with a very low current. Connecting a temperature sensor is not required, but possible with some modification of the modules.