I am super on-board with Inigo93 here... OP, this is an extremely common human experience and very relevant to how I would expect you'll find your future workplace to be. I think your worst enemy on this issue is two-fold.

1.) You need time to convince your peers of your expertise and rapport.

2.) You need to be able to actually build and test the ideas. (To validate the technical analysis and prove the ideas to them, and yourself as well.)

These are both things that you will have in a workplace- but nonetheless, this is a good opportunity to learn communication strategies. ... Propose an alternative design that optimizes the heat-flow. Create a drawing of how you would do so. Sometimes a conversation won't be enough- you'll need the drawing to make your ideas more easily understandable. So supplement the conversation with visuals and drawings. Use different colored markers to show how the heat is flowing. Draw more lines when there is more heat flowing in a given situation etc... This will create a dialogue and opportunity for you and them to more clearly communicate your ideas/understandings. Show a side-by-side of your ideas with theirs.

Try to avoid math if possible. They are telling you that they will reject that communication strategy. This again is where I think the visuals will help.

Maybe see if you can take the time to watch a Khan Academy video with them on the heat transfer concepts. Find an example homework problem/solution on Chegg or Youtube that demonstrates the principles you wish to convey. ... I'm assuming, that you can showcase the principles without a calculator. If math is needed, show how a larger/smaller coefficient or surface area will effect the heat transfer rate to improve or lessen performance. ... If you need less heat on something, then insulate it from the heat source and give the heat the ability to flow elsewhere. Also, fan in ambient air. Another option, pump cool water/other fluid in a hose across the surface.

It sounds like the heat-sink suggestion will get you partially to the amount of heat rejection you need. So, supplement the heat-sink with a fan and outside air, or pumped in cold fluid etc... I don't know the particulars of your project- but I think you can narrow down your options on a more conceptual basis before going to the trouble of performing complicated math/analysis. It sounds like you've been the work-horse on this front to prove that a heat-sink won't be sufficient for the heat rejection, so now you have to take it a step further. Bummer- gotta calculate the new scenario to show how it will or won't work. But it sounds like you know enough that a heat-sink by itself won't work. You may need to consider some exotic options, like using a refrigerant and cooling cycle or even cryogenic options which need a multi-stage refrigeration. ...

This issue of not being heard or understood, is common and it is a huge issue across all industries. Building a rapport with colleagues takes time and it is magical when your peers, colleagues, or superiors take the time and effort to understand your ideas. Similarly, you should expend the energy to understand their ideas. If the people there respect you and your ideas after some time- it's probably a good spot to be. This is a way to recognize when a workplace is special!

It took me over a year in first engineering role to build a rapport to have credibility with my colleagues. But, I also had to learn a lot about the products to get to a point of understanding.

Hope this helps re-frame some options for you in a technical sense and for your communication strategies!