I've pondered this for nearly 10 years now and really there is little benefit in lifting tiles and laying a membrane. Water is coming from beneath the slab and if you block it at the top it won't disappear, it will make it's way to the edges (the external walls generally) and effectively you have forced something like 50m2 of damp up relatively a few square metres of wall base. This could very probably be far worse a problem than you have now.
The best option (apart from half destroying the downstairs walls) is to let the damp come through slowly and dissipate almost naturally - if it comes through slowly, good and regular air circulation will take it away. Heat is not the only requirement for drying, air movement is more important - hence the need to get the front and back door and all possible windows open as often as possible.
Rob is also right regarding damp/condensation. One of the problems with houses not being used in winter there is that one can contribute to the other. Both however thrive in enclosed environments.