lighting and heating chamber project

Hi, I need some help on a project. Im making a box that can be lit up as well as dry objects. I wanted to know is it possible to connect say 4 T5 tube lights and some sort of heating element (thinking of taking apart a hairdryer, or some sort of IR heating unit) to an Arduino and program it to work for set time lengths? any help or parts guidence would be helpful, thanks,

Sure-- the programming for time lengths and so on is just what the Arduino does well.

Your concern; however, must be with the interface between the Arduino and lights, heaters etc.
The Arduino digital and analog outputs can only source or sink a limited current (20ma I think but check this).
This is far too small to run a heater or a light beyond a small LED. Thus you need a relay of some sort which the Arduino can operate and with contacts big enough to operate the load. There are also electronic devices to do this such as transistors, MOSFETS, triacs etc.

Correction on the 20ma. Just looked it up and an output can provide 40ma, not 20

Solid state relays with opto-coupled inputs is a good way to isolate the Arduino from the power lines.

phoxx: Correction on the 20ma. Just looked it up and an output can provide 40ma, not 20

Just thought I'd add - that's an absolute maximum 40mA. 20mA to 30mA is a better safe maximum. (Effectively, you were right the first time. :) )