My school project will operate on one 3.7Volts lithium nokia battery.

I need a ready made charging circuit. If it is possible something with an indicator that charging is complete. I have several nokia phones I can dismantle for parts and also their charging adapters. I assume the input from the adapter is not fed directly to the battery terminals because of the temperature stuff.

Is there a good ready made cheap PCB i can buy online?

 

Electric radio-controlled model airplanes and helicopters use a lithium battery with from 1 cell (3.7V) to many cells. Ready-made chargers are available for them at hobby stores. Pick a charger with a suitable charging current. Most have a charging-is-complete indicator.