Would the arduino be suitable for constantly monitoring enviromental temperatures, switching on and off relays / dimming outputs? Is it easy enough to program, and get info displayed on a screen? And have everything timed to an internal clock?
I have never done anything similar, but want to make a vivarium enviromental control.
Yup, it would be perfect for this. It is an AVR Micro controller at heart, with Digital I/O, some PWM (for your dimming). Also there are Analogue inputs.
Realtime clock, or just a timer? If it is real time you will need a clock driver. Otherwise is pings along at 16Mhz, and has a few internal timers.