Opposite the Pavilion on the east bank of the river is the tail of a sough on Jackdaw Vein in the riverbank. The late Colin Oakman recorded it in 1979 as ‘a small drain 1 ft. 6 ins. wide and 1 ft. wide, with apparently none or very little water flow’. Allan Pentecost has recorded a trickle of water from the scree nearby. I think the riverside drain is not now visible - at least I could not see it when I looked a few years ago. It must be an interesting vein to have thermal water in it. I have never heard of anyone digging there.
There is also thermal water in Hagg Mine (the blocked entrance just north of the wall of Willersley Castle) and also in Nether Hagg Mine (the big run of flooded workings by Masson Weir in the grounds of Willersley Castle on the east end of the vein from Wapping Mine). Both of these have been surveyed, Hagg by myself and Andy Hayes plus the Sheffield University Caving Group, Nether Hagg by members of Orpheus (at least as far as the cave divers were able to get - it is a seriously difficult place). There has been enormous confusion over the names of Hagg (also called Didos Cave) and Nether Hagg.
You also ask about the water feeding the fishpond etc - most of this comes from the main thermal resurgence that once supplied the baths there. However, some is probably from two soughs there. One of the soughs was recorded in 1913 as being "at the back of Boden's bakery". Does anyone know which shop this was? It was somewhere below Temple Walk. Unfortunately, there has been little exploration done in the Matlock Bath area.
All this is taken from the text of my book on the mines of Matlock and Matlock Bath (which, unfortunately, I cannot get published). It'll end up appearing piecemeal on this website!