How does the different types of fast charge affect a lithium battery on a cellphone in terms of heat?
So-called "fast chargers" convert the input voltage (5V or 9 V) into charging voltage for the Li-Ion battery, which is typically 4.2 or 4.35 V most of time, depending on battery's particular type. The idea of "fast charging" at elevated input voltage is to diminish input losses across charging cable and connectors by having "more voltage at less current", the same idea as is used in high-voltage AC transmission lines in common electrical grid.

Having less losses on input side, the "fast charger" can deliver higher current to the battery, in order to charge it "faster". And higher current produces more heat inside the battery (heat gets generated from parasitic internal resistance of the battery), and from DC-DC converters (higher voltage difference is less effective, and higher currents on output side also generate more heat. So the "fast-charging" smartphone usually feels quite warmer than when charged in ordinary mode.