Possible for a short time frame during an eruption event, but highly unlikely during a long time period.
little blurb I found through google on the cooling of lava:
The lava is assumed to be at 1000 degrees C and the water is assumed to be at 10 degrees C. The final temperature for the lava and the water is assumed to be 100 degrees C. These numbers are only approximate. The actual specific heat and latent heat of fusion for lava varies depending on the mineral composition. In his piece “Cooling the Lava”, John Mcphee gives a figure of 1.7 kg of lava cooled per 1 kg of water. My calculations show 2.7 kg of lava cooled per 1 kg of water.
Water has a couple properties that leaves it quite unique in this space..it takes a lot of energy to warm up water compared to most other materials, including lava. You would need around twice as much lava as water to get the water up to a boiling point...and by that point the strait between your two volcanoes would be a filled land bridge.
The water has a lot of methods of cooling itself. The tide and ocean currents wouldn't leave the water in between two islands static (some of the strongest ocean currents exist between two islands)...it would be ever replaced as the current moves and the huge depth of the ocean has tons of room to absorb this warm water.
Wind also comes to play. As it blows over the surface, water evaporates. The act of evaporation for water takes an incredible amount of energy out of the surrounding environment (blowing on your hot coffee is the same principle). So the water at the surface would be consistently cooled.
It is possible to have these conditions right for a short term eruption event to increase water temperatures, but nothing that would be permanent over a month timeline. You could probably make a few alterations (isolate this water from the ocean) that could make this scenario a bit more likely.