What is the average temperature and rainfall of an estuary?
There is no one answer. The temperature and rainfall will be as variable as they are for any other landform. It also depends on whether you mean the temperaure of the water at the bottom or top of the column, the mud or the air.
The temperatures of some estuaries in Alaska are obviously well below 0oC since they freeze over in winter. The air temperature of the Amazon estuary will get to over 35oC (near enough 100F), while the water temperature at the bottom o f the column will probably be well below 15oC simply because the water is so deep. Conversely shallow estuaries with slow tidal flows and little freshwater inflow in tropical areas can have water temperatures >30oC at the surface and achieve a situation where water is evaporating much faster than it is entering.
Added to this an estuary can be a huge chunk of land. The estuary of the Amazon for example could be many hundreds of square miles depending on how you care to define it.