Li-Ion Battery Charging Board Temprature (Junction Temp)
The max Tjcn is 145’C but every 10C rise above 25’C ambient reduces life expectancy 50% approx. 

Jcn to case Thermal resistance (Rjc) for a TSSOP8  is Rjc= 60’C/W and Rja=130’C so design with 1A on battery at 3.6V has a 1.4V drop=1.4W .

There is more loss at lower Vbat initially so your operation is (expected) or normal but a better design dissipates heat thru large copper plane thru the TSSOP leads or has a mini alum. Heat Sink bonded to lid.  

So your junction temp, Tcjn, rise may be twice the case temp, Tc without these improvements.  

It’s your choice. Lots on Amazon may be found.

It’s cheap and so are heatsinks but they shave every penny off costs.