There is another factor not yet mentioned contributing to the effect you notice: global warming is related to the total cumulative amount of CO2 in the atmosphere, not to what we are emitting in this instance. The atmospheric lifetime of CO2 is estimated to be of the order of 30–95 years, i.e. if we stop emitting now the warming will continue into the future before reaching a peak and declining.
If you look at the Mauna Loa graph in Gordon's answer: the warming in year X is not related to the Y-value for X, but to the total area under the graph
to year X.
Quoting from e.g. the PDF Cumulative Carbon and Just Allocation of the Global Carbon Commons:
Recent research has shown that the magnitude of climate change, as measured by global mean warming, is very well characterized by a simple metric
known as cumulative carbon. Cumulative carbon is simply the net carbon
emitted globally over the period of time during which human activities continue to contribute a net input of carbon (as CO2) to the Earth system –
more or less the duration of the fossil fuel era. The key results regarding cumulative carbon are as follows:
• The global mean warming is linearly proportional to cumulative carbon.
• The amount of warming at the time emissions cease is nearly independant of the emissions trajectory over which the cumulative carbon is emitted.
• The amount of warming at the time emissions cease persists for about a thousand years, and declines only very gradually over the next ten thousand years, and still more slowly over the following several hundred thousand years.
Other significant greenhouse gases, notably methane, also contribute to
global warming, but these do not merit consideration on an equal footing
because their persistence in the atmosphere is so short. For example, methane has an atmospheric lifetime of only 12 year, so that we can
delay methane controls for two centuries if we wish, and still get the full
benefit of reduction of methane emissions within a few decades of implementation of controls. The same cannot be said for CO2, as we shall see shortly.
BTW The methane disappears by oxidation, with one of the reaction products being .... CO2 again.