Those lights and where they are positioned should not increase your temps much at all not that LED's impact tank temps like T5's or MH. Are your temp issues new or did they develop over the past couple of weeks now that the outside temps are hitting 95+? What kind of heater are you running and what is your base temp set at? Have you tried reducing your set temp a degree or to?
It looks like the tank is near the front door, what direction does your house/apt face? If it or the wall your tank is on faces west and is an external wall it's likely that the temp climb is due to radiant heat penetrating the walls/door after getting blasted by the sun in the late afternoon causing your tank's temp to climb. Another possibility is if there is a window near the tank that get's a lot of sun and could also be an unexpected source of heat.
As far as the Nest.. There is a better unit that does a lot more that has additional sensors that you place on opposite ends of the house or in a specific area. Once programmed you can have it set to where it will run the A/C unit until the entire house is at the set temp or to a specific room is. You can even add register vent controllers to it so it will automatically adjust airflow to different areas of the house to cool a specific room or area.
Ecobee4.
https://www.ecobee.com/