Anything is possible, and in my opinion, going on a ebay-hunt is often a guessing-game since pretty much anything ive bought there has been without manual, instructions or similar, a picture with pinouts at best.
If one already posesses the knowledge about the components, then its of course a far lesser problem, but ive spent my fair share of life-lesson-money on ebay..
Regarding the original question; Yes it would be easier with manual control.
But then again, ask yourself this; would it be as much fun?
Would it be more fun if you built a timer yourself?
Do you have the time and patience (and other pre-requisites) to learn?
If yes, yes and yes; then please feel welcome to try, we´ll help where we can.
But be prepared for some "life-lessons" along the way to success...
To step between "modes" can be somewhat tricky, depending on what youre controlling..
But if youre heating a enclosed volume that you wish to be at a set temperature, you can heat it for X amount of time, then leave it off for Y time before repeating.
You can then adjust the X/Y values along the way with feedback from a temp sensor, keeping a constant temperature (or at least between two values).
In any way, the arduino can control pretty much anything as long as you wire it correctly, in your case it would be with a relay or a mosfet, if the load is small enough.