The emergence of cyanobacteria caused removal of carbon dioxide from the atmosphere, resulting in Earth becoming cooler. That perhaps implies that the Earth's oceans would have boiled off (in billions of years) if life like cyanobacteria didn't evolve. Is it true?
Short answer: no. The life does contribute to the amount of CO2 in the atmosphere and the temperature on the Earth but mostly not by photosynthetic organisms.
The main mechanism, which regulates the temperature and removes CO2 from the atmosphere is silicate and carbonate weathering cycle. In simple model the more CO2 you have in the atmosphere, the more acidic is rain water. More acidic rain can dissolve more of silicate and carbonate minerals and the dissolved minerals are carried to the ocean, where they either precipitate or are used by living organisms to create shells of CaCO3 (calcite) or SiO2 (opal). When these organisms die, many shells are dissolved but some shells fall all the way to the sea floor and are buried.
In simple words: more CO2 -> more (acidic) rain -> more weathering and C02 removal -> more mineral deposits -> less CO2 in the atmosphere -> lower temperature -> less rain
If you want more information with formulas, I suggest looking up for description of carbonate–silicate geochemical cycle.