He is in his secret lair to the right in the Processing Room of the Carrot Factory, served by drone slaves and protected by a robot security system. Dr. Hare, the evil genius, is building a Giant Space Rabbot to control the world, and using the carrots to make rocket fuel.
Once you enter the factory and free his drones from their Rabbot Ears, you can see him in the Launch Room and ruin his evil plans.
(see related question)
He is in the carrot cake factory
The closed Carrot Cake Factory is to the right side of 24 Carrot Island. You will need a crowbar to get in through the sewer pipe at far right. (see related question)
It is rolled up in one of the boarded windows atop the Carrot Cake Factory. It shows how you can get to the various rooms in the factory. (see related question)
The "carrot blender" on 24 Carrot Island is a factory machine that formerly created ingredients for carrot cake. It has been altered by Dr. Hare to make rocket fuel.
Before you go to the Carrot Cake Factory to the right of Main Street, you will need the crowbar, which you can get for returning the lost cat to Charlie's Carrot Surplus. Then at the factory, you need the blueprints found by the window near the roof. Then you can enter the factory. (see related questions)
The tunnel runs from the water to the factory floor. Pick up the Carrot Transporter and get past the trap doors and the rat, and turn on the power to the factory. (Switches : down, halfway down, down)
Its a carrot cake served in ugoslavia. :)
Return the missing cat to her owner at Charlie's Carrot Surplus and you will receive a crowbar, which will come in handy when you next travel to the Carrot Cake Factory.
The drain pipe is to the far right and down, on the far side of the Carrot Cake Factory. Once you have a crowbar, and the blueprint from the window near the roof, you can enter the factory. (see related question)
You can make carrot cake with or without nuts. If you want them, pecans and walnuts work well.
The swamp or drainage area is to the right of the Carrot Cake factory, and is not an area you can enter. The only important location is the "drain pipe" which exits the factory. If you get the crowbar, this can be opened to allow you to enter the factory where the scheme is being perpetrated. (see related question)
Spreading out the hot carrot cake increases the surface area of the carrot cake. When more of the carrot cake comes into contact with the surrounding air, more heat can travel from the carrot cake to the surrounding air. In this way, the carrot cake cools faster.(This is the exact answer! Did lots of research to find this much information!)