What controls the acidity of the ocean? I have learned that:     


coral reefs are made up mostly of calcium carbonate 
coral reefs are mainly distributed in the tropical zone
The calcium carbonate will be decomposed in the reaction as follows:
$$CaCO_3 + H_2CO_3 -&gt; Ca^{2+} + 2HCO_3^-$$ 


Thus this reaction will be promoted in the environment with low pH. 

The ocean in the tropic zone should have lower acidity (higher pH) for the coral reef to exist.

But in my opinion, the pH in the ocean is determined by the dissolution of CO2, and this process might be promoted in higher temperature?

How to explain this issue?
You have focused on corals (that have a much more lower biomass than for example foraminifera), and you have forgotten what controls carbonate levels at oceans at bigger scale is Henry's Law:

&quot;In chemistry, Henry's law is a gas law that states that the amount of dissolved gas in liquid is proportional to its partial pressure above the liquid . The proportionality factor is called the Henry's law constant&quot;
Source: Wikipedia

So answering your question what controls acidity on oceans is indeed carbonates, but it is atmospheric $\small\sf{CO_2}$ levels (and temperature, as Henry's constant is temperature dependent) what determine the concentration of carbonates.
The quaternary increase of $\small\sf{CO_2}$ leads to the generation of new $H^+$ and thus acidify the ocean, acording to the reaction:
$CO2 (aq) + H2O ⇌ H2CO3 ⇌ HCO3− + H+ ⇌ CO32− + 2 H+.$