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of course you can also look at it as bigger powerplant produces more heat because it allows you to run bigger modules that produce more heat AND dissipates more heat, but the relative rate is the same.
Using a 2A powerplant gives you the same heat efficiency (and thus, a cooler ship) as a 5A powerplant does. If you aren't using much power, it's better to take a low-class but high-grade powerplanet like a 2A instead of say a 3D or 4D.
Complicated answer:
Each megawatt of power used by your ship generates a certain amount of heat. The grade of your power plant determines it's heat efficiency, which is used to determine exactly how much heat is produced per megawatt of power used. Also I mean power USED, not GENERATED. Only power used to power a module generates heat.
If you compare a 2A power plant to a 5A power plant, they both have the same heat efficiency. However a ship using 9 megawatts of power with a 2A power plant generates less heat than a ship using 20 megawatts of power with a 5A power plant. About half as much.
You can improve the heat efficiency of your power plant by engineering it with the low emissions modifier, which can make it even more efficient than the stock grade A level. Meaning the same amount of power used would generate less heat.
What makes this even more complex is that each ship has a different heat capacity, meaning some ships reach their limit and overheat more quickly than others.
https://forums.frontier.co.uk/showthread.php/286628-Research-Detailed-Heat-Mechanics
So a DBX with a grade A low emissions power plant would take the longest to overheat, and a Hauler with a grade E overcharged power plant would overheat the fastest.