heating a pool

It is spring break, so we are at my parents house for a couple of days. The kids like it because there is a pool, a heated pool even. It really isn't that cold outside, but yesterday the water measured at 62 oF. So, with some help from the kids, we cleaned out the pool and turned on the heater. We also put a cover on it, hopefully to help it heat up some more. This is perfect for a quick calculation. Is it reasonable that the pool could get up to a swimable temperature by tomorrow? Let me first make some assumptions and data: 15,000 gallons of water in the pool. This is about 57 m3.…