Is any of the flooded area carpeted? The bottom broke out of a water heater once and not only did the water in the tank flow everywhere additional water then added to it because the tank was attempting to refill itself. By the time I found out what happened most of a room that is carpeted and is 30 ft. X 30 ft. was flooded.
I called a local carpet company and they came in and used their high powered suction clearer to dray out as much water as possible and then they pulled up one edge of the carpet and folded it back and then raised the carpet some and put a series of high powered fans that then blew air under the carpet and over the padding.
The two problems, if there is carpet involved, is the padding can break down if it remains wet long enough and the other problem is mold. So the thing to do if at all possible would of course be to dry the carpet as fast as you can and that means getting moving air between the carpet and the carpet pad.
A, or several, dehumidifiers would be very good to use if you have access to one or more. If you have ceiling fans in the room leaving them on will also help slightly. Any increased amount of air movement will help to some degree even if it is only above the carpet instead of between the carpet and the carpet padding.
Depending on what sort of heat system you have it may or may not help. If you have natural gas or oil that produces a dry heat and by turning up the temperature it will dry out the air more and that will help to speed things up. If you have a heat pump, or like me more than one heat pump, don’t bother to turn it or them up because they do not produce a dry heat and when heating they do not dehumidify like heat pumps do when in A/C mode.
If carpet is not involved the mop suggestion should handle things.
