Greetings,(posted 8303 days ago)I'm not aware of any inexpensive water control devices that will work automatically. When you first turn the water on, the temperature will vary until your pipes heat or cool and reach a balance with the supply, pipe and ambient temperatures. If you let both the hot and cold water run for several minutes that should equalize the temperatures and then you can balance them to achieve the desired temperature.
In your case it appears that you want a colder temperature than is available from your supply. That requires a more elaborate setup. The easiest, but most costly method is to install a water chiller. A homemade solution might be several coils of copper pipe which are then placed in a bucket of ice. Before you jump through hoops to chill you water, if you're just using this for print washing, then you're better off with warmer water. Prints wash by means of osmosis and that exchange will occur faster as the temperature rises. Though I process at 68 or 75 F., I wash my prints at 85-90F.
Regards,