Cold and Hot Water Proportion

How hot is the hot water? How cold is the cold water? What's the pressure of the streams?

Based on information provided, I'd say the answer is, just the right amount.

Hot water inlet: 85 degrees Celsius

Cold water inlet: ? [That's what I'd like to find from the proportion]

Outlet water: 38 degrees Celsius, 140 psi

Minimum supply pressure: Set to 30 psi

There is no way to measure "cold" as a temp, only degrees of heat.

What is the "room" temperature? This will have an effect on the water's ability to remain at the desired heat level.

I say trial and error, as the temp of your bath begins to decrease you just add more hot water.

It will never be the same valve selection twice, unless you can assure that supplied water temps are always exactly the same.

How hot do you like your bath? I like my skin to turn just a bit red, while my son likes his water less hot.

How far does the heated water travel from the water heater?

How well insulated are your walls?

Winter or summer?

Too many parameters left out.

No insult intended but this is an impossible question to answer.

ROUGHLY what is the adequate proportion for cold water and hot water to mix together in a mixing valve so that one can enjoy a nice, warm relaxing shower?

Its midway between shouting & howling.

With a decent fixture you can achieve flow rate and temperature control. I have mine set to about mid point. In the winter the temp setting is almost all the way toward hot. In the summer it is almost all the way to the cold side. Unless you have a temperature setting to automatically adjust to a set temperature, you still need to make some adjustments. If it is automatically adjusted to a set temp, someone will complain it's either too cold or too hot. Just set it so at the hottest point it will not scold the young or the old alike. The little handle can do the fine tuning.