At what temperature would a hotspot in a cement kiln become visible to the eye?

I think you are operating long wet kilns? If so you could add some chloride to the kiln feed to promote the volatility of the alkalis in the kiln. That will drive more off from the clinker and result in lower alkali content at lower temperatures. However, that may increase your impact on the environment. I would need to know more about your process and situation before recommending that.

Sometimes we need to produce special, low alkali clinker. In order to achieve good results we need to waste all dust from the kiln and to burn the kilnfeed harder than for the ordinary clinker. But in this case we are loosing almost all coating on the bricks. The questions: How and what could we change in our kilnfeed in order to protect the bricks even in case of low alkali clinker?

You are correct the theoretical liquid content of your clinker is very high. The litre weight is also high indicating a very dense (almost fused) clinker. Some Al₂O₃ will undoubtedly be taken into solid solution in the alite phase. Optical microscopy can indeed tell you the true liquid content (and the true alite, belite and free CaO content). There are photographic and computer pattern recognition systems available that will do this for you and eliminate the variation between microscopists. With regard to refractory life the liquid content and its properties are important. The viscosity of the flux is a critical consideration. Too fluid a flux can lead to dusting. These inter-relationships are very complex. To answer your questions properly would require a full and detailed process investigation involving microscopic analysis of frequent samples coupled with detailed process data over an extended period.