I hope the question is not off-topic: I want to know "why" it failed more than how I should use my equipment, even though the questions are probably linked.
The power supply is a 0-3A, 0-30V lab power supply (LABPS23023). I fried it trying to charge a 20AH 3.2V LiFePo single cell battery. I had set the supply to 3.8V for the initial charging as recommended, and the current limitation pot halfway (~1.5A, way below the max recommended 1C). Since the battery was only 3.3V stock, and that the power supply had both voltage and current limitation, I thought I would be safe.
Result = heavy instant smoke in the power supply. Not even a blown fuse.
Did the battery "feed" power into the PS instead of the opposite, and the latter would be seriously unable to withstand it?
I highly suspect my understanding is both naive and incomplete. Would a simple heavy duty diode have protected the power supply, but would it be charged in this case?
The schematics of the PS is here: 
Best Answer
Mea culpa, well, sort of. The flyback diode was dead (V32 on the schematics - no fuse indeed), and it was short-cutting the output, hence the smoke also above in the circuit. I replaced them and it worked again.
Now for "why": I have two of the same 20AH LiFePo battery. And one packaging is plain wrong! Yes, the plastic wrapping with the label is the other way round: inverted positive and negative terminals. I had probably double-checked with one, and assumed that the other was alike. I am going to yell loud at the supplier (a well-known company though). It could have cause fire, with such currents. Amazing.
Conclusions:
Bonus: I replaced the SMT diodes (1N5402) by even more powerful diodes (31DF, 300V,60A peak) + fixed them with silicone so they would not even unsolder themselves on a terrific case (like here I guess).