Of course there has to be a direct relationship, since some of the combustion gases from internal combustion vehicles and thermoelectrics are gases containing heavy metals, such as mercury, arsenic, cadmium, vanadium and nickel.
Anthropogenic activities (industries, energy production, etc) produce CO2 which cause global warming. At the same time, those anthropogenic activities produce heavy metals and disperse in air, water and soil...eventually those heavy metals will accumulate in the marine environment (i.e. sediment). It will be interesting to find out which heavy metals give good correlation with climate change.
This relationship may not be tight for all heavy metals. Think of mercury, the occurence of which correlates with mining more than with climate and the toxicity is particularly high for the methylated form.
Whether there is climate change or not, the concentration of pollutants into the marine environment depends mostly on the anthropogenic activities. Heavy rains will wash away all the pollutants from industrial and agricultural activities, ultimately discharging into rivers and oceans. That's why mitigation of pollution activity is so vital in the water resources conservation and management.
Yes in some cases Climate change can influence heavy metal concentrations, and therefore (bio) accumulation in the environment. A change of climate, such as reduced rainfalls can affects the concentration of heavy metals in water bodies such as dams. Basically the less water you have in a dam to dilute the pollutants the higher the concentration! Increasing temperatures also increase evaporation rates of rivers and dams, leading to increased concentrations of pollutants that are dissolved in the water bodies. Some phenomena such as "lake turn over" which is basically the mixing of water in a water body due to convectional currents are highly seasonal. Lake turnover is mixes water bottom and top layers of a water body and therefore increases the suspension or solubility of sediment bound metals. This exposes aquatic organisms to to higher levels of metals (metals are safer stuck in sediment that when in water).
Particulate matter suspended in atmosphere from human activies are washed down by torrential rain into the water bodies.These particulate matter house a lot elemental pollutant.Finally,particulate matter is hygroscopic in nature.