We had a leak going into our ceiling. Luckily, as a wood turner, I already own a moisture meter. This can test the moisture content of wood (but other similar density substances too) merely by pressing a button. That meter worked very well for my problem. Of course, if you do buy one, I don't expect you will find many other uses for it than catching an occasional leak, but it can still be cheaper to buy one than to pay someone to make a simple reading for you. Just store the meter after you are done with it with the battery removed.
It will take several weeks or even months for a ceiling to dry out. This depends on how enclosed the area is, and whether there is still water getting in. Readings made over time should be decreasing. If not, there is still a problem. The moisture content of even dry wood will be around 8%. Check other walls in your house, because this number will vary by where you live, and what time of year it is.
There are several styles of moisture meters. One relies on pins that must be inserted into the material, testing electrical conductivity between the points. As such, it will leave small holes. Better are the styles that do not leave a hole, but they are more expensive. Note that the cheaper models use a probe. This probe will have pins to stick in the wood.
By the way, while the ceiling is still damp, stains WILL continue to spread by capillary action. The water will continue to wick the stain further away. 2 months later is a long time for new stains to appear, however, old stains can bleed through new paint. You may wish to use a product like Kilz to seal in those stains. But wait until it is surely dry before you paint. This is where the meter will help you out.
There are a few possible reasons:
Some hot water recirculation systems use the cold water as a return. In these systems, warm water is returned in the cold water pipe until hot water reaches the the temperature valve that controls the recirculation. Or, perhaps the one-way valve near the pump is failing.
Hot water pipes could be touching a cold water pipe (probably near the water heater). The two pipes touching would heat up the cold water pipe.
Cold water pipes could be touching a ventilation duct. In the winter, the duct would be warm and would heat up the cold water.
No heat trap in the water heater inlet. Hot water might flow up out of the water heater into the cold water pipes.
In the morning, try to feel which parts of the cold water pipe are hot, and that'll be your answer.
Another thing to check, but is likely unrelated, is the condition of a water expansion tank (generally mounted near the water heater) if you have one, or contemplate installing one if you do not (they're needed if you have a pressure reducing valve or a one-way valve in your water meter).
Best Answer
There is nothing about this condition that by itself suggests a leak. Common causes are your cold water pipes run near heating ducts or the furnace, or water from your hot water heater expanding back into the cold supply.
Likewise, a warm spot on your floor could be from ducting, a light below, the sun hitting it through a window, etc.
If there is a leak, sooner or later you will see signs of water - drips, stains on the drywall. If you do don't see any of these, I wouldn't worry.