Is not the purpose of the paint to provide a smooth surface, which in turn creates less friction? I believe this is where the advantage lies in using paint. If you think about it, less friction equals less heat.
I don't know what difference it would make, but I think this is where paint will allow for a more fluid air flow.
A good amount of the heat experienced on a high mach flight is from adiabatic compression. In other words, the rocket compresses the air in front of it before it has a chance to get out of the way since it is compressed without increasing much in volume the temperature of the air increases. This will happen no matter how smooth your rocket is. So if you really polish your paint well you can reduce some of the heating can be mitigated. However, if the paint gets overheated, or the forces on it is stronger than the adhesion of the paint; all of your gains will go away rather quickly. This could be a problem if you were solely relying on the smoothness of your paint to save you.
There is a nifty physics demo that you can do related to this. If you take a large syringe with the end plugged and put a piece of lint or paper in the bottom. Push the plunger in as fast as you can and you can sometimes make the paper catch on fire.
Then why am I hearing from people to paint the rocket with heat resistant paint? Are these people just not knowledgeable? Isn't the idea to paint used to protect surfaces? And if the surface is involved with heat, then heat paint is more resilient.
It depends on what your goal is. If you goal is to make sure your rocket continues looking good, and you are not worried about the heat compromising the structure of your rocket. It might makes sense to use heat resistant paint, since it will be less likely to discolor or boil. So your rocket will continue to look good.
However, if you are to the point where you are aiming for high mach levels I don't know of any paint that will survive a high mach flight untouched. Your ceramic coating has a chance to actually survive the high mach flights there is a problem though. The sub-straight underneath your paint likely wont. If it's fiberglass the epoxy will likely boil or outgas from the heat, this will create an air pocket under your paint which will force out the paint into a bubble shape. The protrusion will then get stripped off by the friction forces and you now have a good sized hole in your paint job.
Now that scenario is a bit hypothetical since I haven't actually tried that coating, but that is a possible failure path.
It's easier to think of the heating problem like this. The entire issue of heating on your rocket is impacted by two things. The total amount of heat that will be generated, and in what space of time it will happen in. You approach things differently if you are going to get a large amount of heat over a long period of time versus a large amount of heat over a short amount of time. In our case, we get a ton of heat over a pretty short amount of time, coupled with a pretty large amount of force acting on the surface.
There are a few ways you can deal with it, in general terms they are:
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Insulation (stopping the heat at the surface)
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Absorption (absorbing it into the structure)
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Removal (getting rid of the heat in some fashion)
These aren't the technical terms that you would find in a text book, but they mostly describe what is happening well enough.
The method that you are currently attempting with your ceramic coating is
Insulation. The problem is I don't believe that your ceramic coating is insulating enough, for how thick the coating is, to keep the heat away from the structure. If you made the coating thicker (ie MUCH thicker ~.25" or more) you stand a pretty good chance of keeping the heat on the outer surface of the rocket. This would probibly wiegh a ton if you used a coating this thick. The only materials that I know of that are suitable for this application is Aerogel, Carbon Carbon ceramics, and a few other exotic ceramics. Most of which are horrendously expensive or at least horrendously expensive to process into a nosecone shape, and in the case of Aerogel has kinda poor properties with regards to friction. So for the most part in amateur rocketry no one really goes for the insulation method, or at least successfully.
For absorption, it's the opposite of insulation. In this case you use the nosecone as a heat sink, and build from a conductive material. You rely on the high temperature handling properties and the thermal mass of the material to evenly spread out the heat throughout the whole structure. This gets a little complicated because everything connected to it needs to be able to withstand the temperatures as well, but it is a valid approach. Making your nosecone out of aluminum would be an example. The heat spreads out through the aluminum, slowing the temperature rise enough to generally get out of the atmosphere before any critical temperatures are reached. Making your nosecone out of inconel would also work. This approach tends to be a bit heavier than some, since most conductive, high temperature materials tend to be heavy.
The last approach in my list is removal, where you are trying to remove the heat from the structure entirely. There are many ways to do this as well. You could spread a film over the surface of the rocket to boil away and remove heat from the rocket. You could have cooling channels in the nosecone and circulate coolant through it to pull heat away. Or you can put a coating on the surface that will ablate away, meaning solid -> liquid -> gas -> sometimes plasma. This usually happens almost instantaneously, and since it undergoes 3-4 phase changes it removes a considerable amount of heat in the process. You also want this ablative to be insulating since you only want the outer surface to ablate, and not the whole coating at once.
Most rockets that I have seen either use materials that can absorb the heat and handle the temperatures reached, or the put an ablative coating on to protect the nosecone underneath. Ablatives can be much lighter overall, however they usually require more work since you have to reapply the coating each time you use it. Aluminum is kinda nice since you just to do it once and your done. But it is heavier and has its own problems.
Here is the ablative that I am planning on using.
It is very expensive, and a little bit hard to obtain (Its aerospace related so sometimes extra paperwork is required). So I don't know how much use it is to you. I have seen some expired stuff on ebay pretty cheap (mine expired in 2006), but new from corning it is about $350 for a kit; though a 5lb kit will probably go a long ways for a 4" nosecone you could probably paint it a hundred times. But its good for about 6000° F and can still go down to -40°F which is a bit important for where I launch. I am still not quite sure it is the right stuff to use, it's pretty thick. We typically use it for coating launch stools for orbital launches to protect it from the rocket exhaust. We do have to re-coat the stool before each launch. But it definitely does it's job well, I'll just have to see if I can apply it well enough.
Don't take this to mean this is the only stuff in the world that will work. Not even close, there are countless ablatives out there, I just happen to have this one.
