If the heat sources you are using DO NOT have grounds on thier cords, then it does not matter if the ground going to the power strip is hooked up or not(remember, if you do not hook up the groung to the power strip, you should never plug a grounded plug into the strip). I would deffinately make sure that the stat is grounded though, if you choose not to ground the power strip(because you will most likely be touching this and don't want to make yourself the ground had you had any problems). In short, it is never a bad idea to ground anything that has to deal with electricity. Would I ground it? Yes!! If it is there....Hook it up! Why not? Hope this helps
Disclaimer: I am not telling you to not hook the ground up! All I am saying is that it is not necessary to ground the strip if the heat sources or other loads do not have grounds on them.