Plants build three-carbon sugars during photosynthesis by fixing a CO2 molecule onto a two-carbon chain with an enzyme called RuBisCO. In a typical "C3" plant, this happens relatively directly. But RuBisCO can screw up and fix an O2 molecule instead, and the erroneous result costs the plant energy to repair.
As the temperature rises, so does the error rate. At a high-enough temperature, the plant loses energy overall, which it can't survive long term.
C4 plants separate this process into two steps spatially. They build a four-carbon molecule in a much less error-prone way, then move this to a part of the cell where it's broken down into CO2. RuBisCO is again used to build the three-carbon sugars, but because the relative concentration of CO2 to O2 is so high, the error rate is low. There's some additional overhead to this process, but it pays off in warm climates.
Incidentally, there's another warm-climate metabolism: CAM (crassulacean acid metabolism). CAM works by temporally separating parts of the process. At night, they open their stomata, and use CO2 to build an acid. During the day, they close their stomata, cleave CO2 off of the acid to increase the concentration, and let RuBisCO its thing.
I believe RuBisCO is the most common enzyme on Earth by weight. I find it striking that Mother Nature has had to find all these hacks to get around its shortcomings, but hasn't found a way to simply fix the enzyme so it doesn't make so many errors.