In high light or high temperature C3 plants undergo photorespiration, which essentially is a deviation from the normal RuBp+CO2+H2O --> 2PGA --> calvin cycle because carboxylase (the normal enzyme that fixes CO2 into the calvin cycle) doesn't work.
When photorespiration occurs an O2 molecule reacts with the RuBp with the help of the oxygenase enzyme to create CO2 (which is lost), and 1PGA molecule that is fed into the calvin cycle. Since CO2 is lost in this reaction it is called photorespiration. Ultimately it is this CO2 loss that makes C3 plants bad in high light+high temperature environments.
C4 plants get around this problem by converting carbon to malate, then a CO2 molecules is split off the malate and fed into the calvin cycle. This prevents photorespiration and the loss of carbon from the system, making C4 plants efficient in high light + high temperature environments.
While it is true that C4 plants are more efficient at taking up CO2 than C3 plants this does not mean they will grow better than C3 plants under all conditions. CO2 uptake in C3 and C4 plants depends upon light, CO2 concentration and temperature. Each type of plant does better in its respective environment. C4 plants produce more sugar than C3 plants when the temperature increases and the light increases. But when the light intensity is decreased and the temperature decreases C3 plants produce more sugar due to increased photosynthesis. See graph below.
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In addition, there are 2 points that each plant has with respect to growth. One is called the light compensation point (LCP), and the other is called the temperature compensation point (TCP). The LCP is the point at which the amount of light provided lets the plant photosynthesize exactly enough to live, but not to grow or reproduce. This point is where photosynthesis exactly equals the rate of respiration. The other point is related to the fact that for every 10 degrees Celsius change in temperature respiration (sugar breakdown+O2 usage) increases by a factor of 2. Therefore, the temperature compensation point is the point at which respiration has risen to a point that exactly equals the declining photosynthesis reactions (because as temperature increases near the protein's maximum limit it causes them to denature and they aren't as efficient). Anyway, what this all means is that each type of plant C4, and C3 has a different temperature and light compensation point, so under the same conditions a C3 plant will be more or less efficient than a C4 plant depending on what the conditions are (i.e. C4 plants have higher light and temperature limits, than C3, but C3 plants are more efficient at lower light and temperatures). See below
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On land, I know that C4 plants on land don't start growing faster when more CO2 is added to the tank because they have smaller and fewer pores on the surface of the leaf. They have these traits because it helps them cut down on water loss in dry, hot, high light environments (it also helps them recycle CO2 from their own respiration processes). Now this may not be the case with aquatic C4 plants because they absorb CO2 through tissue contact with the water and don't need to absorb it through their pores like C4 land plants, but it is interesting nonetheless.
Also just for interest sake I'll list some advantages/disadvantages and facts about C3 and C4 plants that I know below:
1) Low light + low temperature C3 plants = more suited
2) High temp + high light C4 plants = more suited
3) C3 photosynthesizes more with more CO2 (at least on land)
4) Some C4 plants have reduced light reactions to prevent damage to the photosynthetic mechanism in strong light
5) Not all C4 plants operate at the same photosynthetic level
6) C4 plants are able to utilize the CO2 from their respiration processes more efficiently than C3 because of reduced stomate size and number.
I hope this clarifies what I was trying to summarize before
