Only UVB rays will provide the health benefits your turtle needs in terms of vitamin D, so you'll just have to wait the 6-8 weeks... your turtle will be fine for then, although I'm sure it is annoying to have to buy a new one again
As for heat bulbs, using a regular house bulb is perfectly fine, that's what most people on here do.
The water temp is fine, but if the ambient air is too cool, your turtle won't bask so a heat lamp is a good idea.