I tried this circuit & it works but I have a thermal issue with it. At any reasonable charge current 0.3 or 0.4A the LM317 overheats. It's probably because I'm running this from a 12V external DC supply

Power is as power does. The power in ANY linear circuit is:

P = (Vin - Vout) X current


If you use a cheap buck switcher, you will have to modify it so that it does CC (constant current) when the batt voltage is below target value then goes into CV (con voltage) to hold it at the target value.

 

Just don't forget to charge that thing on a non flamable surface , especially when using your own charger . Might go on fire if your voltages/and or currents aren't accurate

 

The LiFePo batteries don't catch fire, it's the Li Poly types known for making bonfires.