If it's not connected to the heating it may be difficult to keep warm enough with even a room heater - especially in winter; i'd recommend testing it before you actually get the hedgehog, just to certain, especially if your parents don't want the hedgehog indoors.
Additionally, hedgehogs are nocturnal; you must be willing to go out to the office when the hog is awake, to let them out for some exercise outside of their enclosure - this is one of the main reasons I prefer having mine in my bedroom, but to each their own.
If your mother is anti-having the hog in the house, make sure that she is absolutely fine with you buying & keeping insects to feed the hedgehog. They *need* live insects (not dried, or canned!) and they need a variety of them at that; typically it is recommended that you have at least 5 different types.