Medieval did they fill a bath???

Greetings one and all!

My focus in the SCA has largely (mostly...) been in the Arts, but this is a science/technology question.  I am curious about the mechanics used in filling up one of the two person (or more) wooden bath tubs that feature in illuminations.  My curiousity was piqued by a mundane situation in our house, our boiler has finally packed it in, and until a repairman can come fix it, we are stuck boiling water if we want a wash.  I decided I must have a bath, and it took 30 minutes to fill our bath to the depth of 3 inches. Now, our bath is a typicall European bath, nice and deep.  That's when this question stuck in my head, as it woud have taken about 2-3 hours to fill our bath at the same rate, and medieval baths appear to be half again as deep, and twice as wide as our bath.  There is the possibility medieval baths contained cold water, however that would not be pleasant for socialising, it could have been that they bathed only in the summer so the cold water would have been welcome,  However I think they loved their comforts as much as we do, besides the nickname "stews" does at least imply that heat was involved.  I've been considering the matter for some days, I did think of a large caldron, but that would still take a great deal of time to heat.  Another possibility is a large cistern constantly filled and heated.....but while a logical solution, I think it unlikely.

Many thanks, good gentles all for any clues regarding this query, I apologise for its frivolity.

They Used Buckets

Although grand tubs might have been large, the average tub really wasn't. A bath was a big deal as it did take considerable time to prepare. Royalty had 'bathmen' who were in charge of the tub. Anyone with servants would have had their baths prepared. The poor did it the hard way. Bath water was heated over the fire or by placing the bath near the fire (which probably took forever but at least you wouldn't get scalded). In summer, bathing might take place outdoors - solar heating, anyone?

Here are a few links:

There were some castles with indoor plumbing but I don't know much about it besides tha the pipes were lead (this may explain a lot of medieval history...)