Hi,
Definitively, it going to cost you MORE money to turn it off and then to warm up the store. The best you can do for SAVING money is letting it low (unless it is an antique stuff and you're scared it takes fire or so), but at work i guess you have a regular new enough heating system.
Also it going to take time to warm the store up again and it can make work the heater too much at one time, i don't believe you want it to break for overworking it each morning week. Because it would cost much more money again to fix or replace it.
When you are not at home, do you stop the heater and do you let it go automatically? If you don't stop it at home, just do the same at work. And it is not too agreable to come in a cold store, also it might prevent mold or humidity if you keep it low.
Hope it helps.
Just wondering what was your point in the debate, stopping or letting it go on overnight?