The issue is that a core i5 CPU has 4 physical cores vs. only 2 physical cores in a core i3 CPU.
That means it has more transistors. Generally speaking, the more transistors a CPU has the more power the CPU will consume because each transistor needs electricity. Newer generation CPUs tends to be draw less power than older generation CPUs especially if the focus is to reduce power consumption. However, when comparing a dual core and quad core CPU of the same generation, the quad core will by default draw more power.
There are a couple of ways to actually reduce the power drawn by the CPU.
1. Voltage Adjustment - All CPUs are defaulted to draw a certain amount of voltage. The voltage and be adjusted up or down assuming the motherboard's BIOS allows you to do so. People have been able to use less than the standard amount of voltage supplied to the CPU, but not all CPUs (even of the same model) can tolerate lower voltages without running into instability issues. Maybe it's possible to lower the CPU voltage by up to 0.1v to help reduce power consumption.
2. A more effective way to lower power consumption is by lowering the clockspeed. The lower the clockspeed the less power the CPU will consume. However, this directly affects performance. One thing you can do is disable Turbo Boost. This will prevent the CPU from automatically overclocking itself. For example, an i5-4670 has a normal clockspeed of 3.4GHz, with Turbo Boost active that can go up to 3.8GHz. Additionally, you can also force the CPU to run at a lower clockspeed, like running the i5-4670 at 2.4GHz or whatever.
De-activating Turbo Boost as well as forcing the CPU to run at a lower clockspeed can be done in the Advanced Power Options. There is a section for Maximum CPU Performance (or something like that). In Windows 7 simply reducing the max performance to 99% will disable Turbo Boost. In Windows 8 you need to set it to a lower value. May something like 90%, you need to experiment. Setting max performance even lower will reduce the clockspeed.
This is not intuitive and you must tryout different frequencies to figure out the affect on the clockspeed. For example, my Lenovo Y470 laptop has a dual core i5-2410m CPU; the normal clock speed is 2.4GHz and max Turbo Boost speed is I think 2.9GHz (using only one core). Setting Max CPU Performance to 99% in Windows 7 will limit the CPU to only 2.4GHz, thus reducing both heat and power consumption. Setting the percentage anywhere between 77% - 98% lower the clockspeed to 1.8GHz. I think between 66% - 76% lowers the clockspeed to 1.6GHz.... Like I said not intuitive and for Windows 8 it works a bit differently.