My product PC board malfunction on moderate temperature
As jippie mentioned, reflow everything. Cold solder joints can wreck thermal efficiency.

Beyond that, lithium batteries are prone to fire hazards so they usually have thermal safety cut offs built in.

My assumption is that you are probably having a "thermal resistance" (Rth) issue. While from a distance, your board probably appears safe, up close, individual components are heating up on a much larger scale. Heatsinks and larger ground planes can improve this, as well as, thicker copper pours for the planes.

If you know the power draw of the failing components, you can easily calculate their temp by multiplying the power by the thermal resistance and adding it to the ambient temp. If you look at the attached datasheet, it gives a thermal resistance of 417 C/W. That means that with a 20 degree safety region between ambient and cutoff, you could only run it at 47mW before failure...

http://www.onsemi.com/pub_link/Collateral/MMBT3904LT1-D.PDF