The temperature drop depends on a few things. Tank size, tank temperature, water temperature, flow rate, and heater size need to be taken into account. On larger tanks the faster flow rate vs tank & heater size negates any massive temperature drops. On smaller tanks it needs to be run in a little slower.
I mix hot & cold tap for my tanks & hose it in. I get a flow rate of about 5gpm wide open, when doing a 50% water change on a tank such as a 20, 29, or 40 gallon there is no way the heater can keep up with the water flow. If the tank I'm working on is 80F, and the tap water is coming out at 50F, in a matter of minutes I've dropped the tank temperature to 65F, pretty chilly for most NW cichlids, which is what I mostly have.
Using hot tap water for a tank safely mainly depends on your water heating & storage setup. Most commonly found in the US a free standing independent gas or electric fired hot water heater & storage tank is used. This water is stored under mains pressure, in a fiberglass lined tank. This is fine to use.
Other systems used overseas include a water heating system tied into the home heating system, the boiler. This water is often recirculated through the heating system, and tapped out for faucet use. This can accumulate some metals depending on how long it has been circulating.
Another system stores hot water in an open tank in the loft, gravity fed to the faucets. These can accumulate bacteria, or anything else that may fall in from the loft.
The only system I have any hands on familiarity with is the first one mentioned, though I've heard enough about the others to have some idea about how they operate.
as I've certainly studied the back&forth in many threads here regarding this little bit of controversy. There seem to be members who are well-regarded as experienced here on TFF (as far as anyone can ever tell) who fall into both camps. I had reached the point of feeling that 25 or 30% changes with cold water would probably be fine assuming you had a reasonably mature tank and not terribly expensive species but I was worried about 50%. Hearing you report your success with 50% is just one more tidbit of evidence that that would probably be ok too in most cases. Of course at some point there must be a "crossover" to it being dangerous since use of icewater is a form of fish euthanasia, right?
