Sea surface temperature anomaly from HadSST3 reanalysis is overlaid for six major volcanic eruptions that occurred in years: 1883 1902 1912 1963 1982 1991.
Calendar months of the year of eruption are aligned, since changes in optical transmission tend to warm winter months in a similar way irrespective of the month of eruption. This is particularly noticeable in the tropical southern hemisphere in the first year after eruption and in land temperature anomalies.
It is notable that the widely reported minimum in temperature, two years after an eruption, seems to align with the minimum of a natural repetition of about 11 / 4 = 2.75 years duration. This means that much of the variation typically attributed to volcanic eruptions is spurious and would occur anyway.
It is also noted that the interval between the two larger peaks at both ends of the record is about 11 years.
To assess the any cooling: the range before eruptions is 0 to -0.2 K , in the following period between 0 and -0.25 . This gives an average drop of 0.025 degrees in the immediate aftermath. It is not obvious whether this is part of a slow long term decline, an initial drop and recovery or a permanent offset.
In any case it is an order of magnitude smaller than the 0.25 to 0.3 deg C usually attributed to these events.
A similar plot from extra-tropical regions here:
A study of the cumulative integral (the long term average) helps to remove the repetitive signal and isolate the volcanic effect: