Designing a 24V DC Wood Burner System With Thermocouple Temperature Control

Hello, 
     I am helping my brother with a project for his class. He is designing a small system similar to a "wood burner", current goes through a metal tip to generate heat. However, the metal tip must maintain temperature  even when exposed to cold, such as ice. 

     I thought he could use 120v power in, splitting off to a voltage controller and DC power supply. From there the 24v dc would run to a small control board that can communicate with the voltage controller to maintain temperature by monitoring a thermocouple. 
     So, as the tip warmed up and approached his set temp, the control board would know based on the thermocouple value and could cutoff or pulse voltage to maintain that temp. When the tip is exposed to objects and loses heat, the thermocouple value would drop and control circuit would tell the voltage controller to give more energy to get the temperature back in range.
     By trade I am an engineer, but work with larger scale panels rather than small circuits.My main problem is I have no idea what these components are called. I am having a hard time researching parts due to the large range of products. I know what I want to do, but am lost trying to find the correct parts.
     So if anyone with knowledge of parts could help me out it would be greatly appreciated, even if its general names. Maybe someone with experience knows of a better design, or noticed any flaws in my plan?

Taylor... I assume you have identifited the heating tip (use a wood burner tip, or a tip form an "instant heat" soldering iron".  You can get small 'bead' thermocouples that you could probably build into the tip.  depending on the voltages you are using, you should be able to find a Pulse Width Modulation (PWM) controller or even and on'off one which will do your regulating for you.reply with a bit more detail on the heating tip and size and voltage, and your desired temperature precision and we can maybe help you more.

Hi David, Thanks for the reply, the pulse width modulator is exactly what I had in mind to control the output power. I have also selected a nice set of small thermocouples that hooks up to a display, so we can track temperature. Our original plan was to run current through the tip and have it automatically controlled. Our budget will not fit this plan and the tip he wants to use it titanium. So now we plan to heat the tip with a heating coil wrapped around the base of the tip, with a thermocouple attached near the very end.I am now trying to select a pulse width modulator/heating coil wire combo. I have absolutely no experience with this, and my attempts to research and apply joule heating equations have been unsuccessful. I have found a few heating coil wires that give resistance levels and wattage at different voltages. I also notice the pulse width modulators have a range of wattage output. I found a really cheap AC modulator but the output goes up to 4000 watts, and im afraid it would be overkill for the wire. Should I use a DC modulator with smaller wattage output, or find wire with higher wattage? Im not sure how the ratings tie in to one another between the wire and modulator. My last question is when I cut this wire, will the ratings change? I'm sure we will only use a few inches to wrap around the tip.

Taylor,Your heating wire will have a certain resistance per inch so when you cut it, the resistance (and power) will be less.

Taylor apologies, I have been really busy (and the time difference does not help...)I cannot believe that you cannot find a suitable tip with heating element from the many available for soldering irons and wood burning applications.  As an example I give this project form Elektor Magazine:https://www.elektormagazine.com/labs/platino-soldering-station-140107
This is a temperature controlled soldering station based on a standard Weller iron element which contains a sensor and a heating element.  Just what you need.  But I don't know if it will exactly suit your needs.  My main point is, unless you are doing something which really hasn't been done before, why reinvent the wheel?  By all means make your own controller for this element, but it might be something that saves you a bit of time.I am not sure if the sensor in this element is a thermocouple (think not) and some of the content may be behind a paywall.  But let me know how this fits with your requirements.