We are restoring some 50 plus year old hard wood floors that have been abused by renters. We are rookies at this and are following the advise of others in the clean-up. There are multiple stains and spots on the flooring. Most have sanded away and some have faded with our application of wood bleach. But there are a few spots that seem to be wet and won't dry out. In fact some days they are wetter than others. When we put cloths over them to "soak up" the wetness, the spots get bigger as if more moisture is being drawn out of the wood as we try to dry it. There are no leaks over or under the flooring, which is a raised floor. So our question is what might be causing the dampness? and how do we dry it out in order to finish the flooring? We've considered putting a heat lamp on the spots, but wonder what this might do to the wood.
Any good advise is welcomed!

It it probably a type of oil. If it was water, it would have evaporated. Some oils never really dry out. You may have to replace those boards.