How to use arduino to continuously control voltage/current?

loveinzurich:
so, how is precise temperature control system implemented in industry?

Exactly in the way you have been told in this thread.

only have on and off two control states? This cann't be true? :~
In industry, temperate control requires high accuracy.

loveinzurich:
only have on and off two control states? This cann't be true? :~
In industry, temperate control requires high accuracy.

Sorry but you asked a question and I gave you the answer. I have worked in electronics for about 45 years now and you do not beleve not only me but all the others who have contribuites to this thread.
As my son would say " have a word with yourself".

loveinzurich:
only have on and off two control states? This cann't be true? :~
In industry, temperate control requires high accuracy.

They are just giving you a hard time. They are saying that even with PWM, there is only two states, but how long it stays in one state or another is the key. If you really want to do it, I won't give you any crap. It's your project. Connect an Arduino PWM pin to maybe a 100 ohm resistor and then to the gate of an N-channel MOSFET rated for the current you want to control, like an IRF260. Connect the MOSFET Source to ground and the drain to one end of your heating element. Connect the other end of the element to the positive supply.

What is it you are doing that requires a time response of 0.1 second?

There is no such thing as one way. It depends entirely on what you are doing. Ovens, heating systems, and cooling systems can be switched very slowly on and off because generally the system has a lot of inertia. Also, switching large loads on and off quickly plays havoc by causing RFI and heat loss due to switching losses. Phase control on large loads causes non-harmonic low power factor, causing line transformer heating.

Lighting control uses phase control, and therefore a PWM that switches 100 or 120 times a second, because an incandescent filament has a thermal inertia a lot less than that of a heating element.

Soldering irons generally use an on-off aka bang-bang temperature control, again because of the thermal inertia of the system.

My house temperature stays fairly constant, within a couple of degrees F of the set temperature, but it comes on for several minutes, then turns off for 10 minutes to hours.

I'm not actually contradicting anything Grumpy_Mike is saying here, at least I don't think I am. If in doubt, go with Grumpy_Mike.

If you try to make the voltage continuously variable, in other words an analog voltage, that requires that you either burn up a lot of heat in a linear regulator or use what is essentially a variable switching power supply, which is... wait for it... On-Off control.