Lucys place fit the bill. We visited family in February and it proved to be a great base. Lucy was readily available by email and quick to respond any questions.
The house is a traditional Maltese home, thick walls , open stair wells to living spaces to keep dwellers cool in the heat.
The houses are naturally more difficult to heat also, we stayed during a cooler spell of weather and an extra layer was needed when indoors...the nature of these houses no reflection on our host. Heat was available via a/c .
We would be happy to recommend Lucys place as a base to explore Malta.