I'm starting to have a problem with overheating and frame rate limiting, to reduce heat would turning the lights off make a difference, or are they very cheap to run?
You didn't specify which lights you are referring to, but I will assume you mean the keyboard lights.
A typical LED consumes 15 milliamps at 3.3 V.
An average Laptop Battery might have the capacity of 4500mah
Suppose your laptop can run on 4500mah for 3 hours, that means that your computer draws 1500 milliamps per hour.
Suppose you had 10 leds on the laptop
Milliamps per hour without leds: 1500
Milliamps per hour with the leds: 1500 + (10 * 15) = 1650
In other words, the leds make no practical difference on battery life. (Few minutes at most).
You asked about heat.
Led's do produce heat, but the type of leds that come on a computer laptop, produce an insignificant amount. They effectively make no difference.
The best bet for an overheating laptop is to take it to a repair shop, and have them replace the thermal grease.
A normal keyboard has holes in it that help increase airflow threw the heatsink so it can effectively transfer heat. With a backlit keyboard you have no extra airflow and overheating is pretty much inevitable. I would honestly recommend removing the backlight from your laptop's keyboard if you are having heating issues.