I wonder if all that can be done by coding
Well unless you have one of those new processors with telekinetic interfaces well no.
I need a "connection" and hardware addition in order to work it out
Well you need a temperature sensor, I would recommend a digital one if it is going to be remote from the Arduino.
Some sort of Real time clock so you know the time and some mechanical or solid state relays to switch the heaters on and off.
You need to know what current your heaters take in order to specify the relay size.
You could also do with some LEDs to show it is working and some buttons and switches to control options.
If your temperature / schedule is fixed then that can be written in to the code otherwise you need a way to program it from the Arduino or an other language like processing.
Finally plan it all out before you start buying stuff.