Well, you have to remember nature always strives toward equilibrium. If the tank is warmer than the surrounding air, the tank will give up heat to the surrounding air. Hotter objects will always give up heat to cooler objects until equilibrium is reached. In almost every case, equilibrium means everything is the same temperature. There are special cases if there are heat sources or sinks, but basically, it means heat will always flow to try to bring everything to the same temperature.
How much room temperature affects the tank is a question of how efficient the heat transfer is. There are 3 methods of heat transfer, conduction, convection, and radiation. Radiation isn't going to be a very large part at all (though it is non-zero, everything radiates at least a little bit!), it becomes a question of conduction and convection. Which mechanism dominates depends on a lot of factors -- how stagnant is the air near the tank? How big is the temperature gradient? Because, if the temperate gradient between the tank and the air is large, the air will get heated up, it will then rise, causing convection -- this is known as natural convection. This is as opposed to forced convection, if the tank is next to a fan or a vent, for example. The amount of heat transfer varies depending on which mechanism is at work, and it is most likely in total a combination of all three mechanisms. We also have to look at the inside of the tank. Water is much denser than air, so conduction becomes a much more important mechanism for moving heat -- but the filter is making forced convection and the water around the heater itself will undergo natural convection.
So, you have to look at each of the following steps. 1) How efficient is the heat transfer from the heater to the water 2) The heat transfer from the water to the tank material (and it matters a lot if it is glass or acrylic or something else) 3) The heat transfer through the tank material 4) the heat transfer from the outside of the tank to room 5) the heat transfer from the top of the tank
So, it is not an easy process. However, in all cases, the larger the temperature difference between the tank and the air, the larger the heat transfer will be.