How to simulate heating coil ?

After a few days of research, I feel quite confused by what tool is responsible for what problem. That’s why I decided to ask here for help in finding out the directions where should I go. I would just like to know, If it’s possible, and what tools should I use.
There are 3 functionalities I would like to achieve (most important first):

  1. I want to create webapp in which users will be able to visualize a coil heater (which look like this):

  2. User can parametrize wire material (resistivity, mass) number of turns, wire diameter, legs length, resistivity, mass, applied power, etc. In return, the app would visualize (or maybe “simulate” is a better word here) the heater with applied power.

  3. I would like to measure temperature and/or heat flux at each place on the coil, or just the highest values globally.

I’ve found this example on gmsh/onelab/getdp stack, that looks very similar to what I want to achieve.
I assume that processing heat transfer on this kind of structure is possible only with finite element solver like getdp.

My current idea is to create a webapp that will send a request to the backend, which then starts python script and generates this kind of mesh with pygmsh. Then process it with getdp/onelab or somehow (here is the place where I don’t know how to do it), and send the processed data back to webapp which will visualize it using vtk.js.

What confuse me the most, is the fact that examples on vtk in action suggest that, vtk alone is able to do this kind of operations, without gmsh/getdp/onelab stack behind.

What is the best way to achieve those functionalities?

VTK/vkt.js excel at showing the results of a finite element solver. Meshing, modeling, and simulation capabilities are not available in VTK.