My assumption is that the steel is oxidizing at the high temperatures and therefore the emissivity is raised, giving you the bump in the heating curve.
Try using the same piece of steel for all tests, so the oxidation and resulting emissivity is uniform between tests.
Or, try using a high temperature ceramic instead of steel that won't oxidize.
On a metal, the emissivity should be higher at the high temperature, so I would be inclined to think that the lower temperature measurements are more likely to be inaccurate than the high temp ones. I would also expect the emissivity to be quite high once it has become incandescent. Also, at very high temperatures, in a room temperature environment, I would expect the affect of reflections to be minimal. I would start by producing the curve using an emissivity of 1, this will plot the change in apparent temperature, which could help in understanding what is happening.
I am very interested in seeing the curve that you have produced.
You may not be able to use tapes, but try a high-temperature paints. With proper surface treatment, there are paints that will withstand 1000 °C. One to try is VHT SP102. Be aware that as some paints go up in temperature, their emissivity changes in a exponetial decay-like fashion.
Thank you for the replies. A ceramic material was my first thought since it wouldn't oxidize. The problem with that is the face of the tile that the torch touches quickly reaches 2000°F while the backside is much cooler. I will try the high temperature paint to prevent oxidation on the steel and if that doesn't work well I'll try a thinner ceramic and measure temperature on the backside of the piece.
I have backdrops around the setup to reduce reflections. When measuring from the same side as the burner, the burner itself leaves a very noticeable reflection. I said I thought the high temperature results were less accurate because I have done the emissivity check with electrical tape at low temperature and the results were consistent with emissivity tables. So if the emissivity is changing at higher temperatures, I would expect those results to be less accurate. Attached is the graph of max temp on 1/8" thick cold rolled steel plate from a propane burner and emissivity of 0.79 (the flat at 1220°F is the top of the temperature range used). The next picture is the same test but emissivity changed to 1.
Gary suggests pre-treating the steel by heating it so that it oxidizes and then using it for the testing. That should remove some of the emissivity variation.
Frank suggests using high T paint. I have done similar and it is a good method, depending on your goal.
You have suggested using alternate materials. I think you will still need to establish their emissivity as a function of temperature.
You state that you want to establish the rate of heating. This will be affected by many factors. I assume you are controlling geometry and flame contact, so that they are not in play. However, the choice of material, the surrounding temperatures, AND the broad band emissivity of the object will affect the rate of temperature rise. The material's properties, including density, thermal conductivity, heat capacity, and emissivity will all enter into the rate of heating. The emissivity will affect things in terms of both the rate of absorption of energy from the flame and the rate of energy loss to the surroundings. This effect will need to be considered if you change the emissivity of the material by, for example, painting it.
Assuming we can keep the temperature of the surface steady and, we can vary Trefl without modifying the geometry of the space, we do a series of thermograms modifying the heat sources, contributing for Trefl on the surface where we want the temperature measured.
T and TreflX are expressed in Kelvin, t and tsurface in degrees Celcius.
Wx=σ∙(tsurface+273.15)4, tsurface= apparent temperature on the surface measured with camera set for 1 at emissivity.