This is a rather interesting article:

http://iga.igg.cnr.it/pdf/WGC/2000/R0868.PDF

In regards to the Fábiánsebestyén-4 well near the Bekes Basin,

In the Fábiánsebestyén-4 well the bottom-hole (4239 m) temperature was 202°C, but the SiO2 temperature was higher - 254°C. This suggests that the produced water migrated
partly from 5-6 km depths. In the case of Nagyszénás-3 well, the SiO2 dissolved in the water at 193-199°C. To research the faults and geothermal reservoirs in the surroundings of Nagyszénás-3 and Fábiánsebestyén-4, magnetotelluric measurements were carried out. The results of measurements proved that there were geothermal reservoirs which were
connected to tectonic zones and went down to 9-10 km depths.

I would imagine Exxon measured the temperature of the water coming out of the Foldeak well. This would give them some indication of where the water is originating from.

The Figure 1 map is interesting. There are areas of "Karstified and/or tetonically fractured rocks with temperatures higher than 150 C" right where they drilled the Foldeak-1, Mako-6, and Mako-7. Hod-1 and the Mindszent-3.

Karstified:An area of irregular limestone in which erosion has produced fissures, sinkholes, underground streams, and caverns.