Changing the heat supply of energy intensive industries from today's mostly fossil sources to nuclear of renewable sources offers the opportunity of reducing greenhouse gas emissions. Many industrial processes require heat at a high temperature level, which restricts the selection of the heat source. The high temperature reactor (HTR) as a nuclear and the solar tower as a renewable technology are technically capable of supplying high temperature process heat, but their implementation on an industrial scale depends not only on the technical feasibility but also on the economic competitiveness to the conventional basically fossil heat supply. In this paper, the economics of the high temperature process heat supply by HTR and solar tower are analyzed and the question whether these alternative systems can compete to the fossil heat supply is answered. The analyses focus on the example process of ammonia production. A new mathematical optimization model is applied which determines the optimal facilities sizes and the optimal facilities operation modes for different energy supply systems. The results reveal that none of the energy supply systems containing a solar tower or an HTR can compete to the heat supply of a heater fired by natural gas. The pure solar heat supply of a constantly operated ammonia plant turns out to be particularly disadvantageous. Moreover, the coupling of the HTR and the solar tower as two capital-intensive technologies is not a sensible option. Under good solar conditions, the heat supply of a constantly operated ammonia plant by an HTR and a fossil backup system turns out to be the best alternative to the fossil heat supply. Only under excellent solar conditions, which occur for example in South Africa, the fossil supported basically solar heat supply is the best alternative system. Nevertheless, even those best alternative heat supply systems can only compete to the fossil heat supply if the gas price rises significantly, in a scope which cannot be expected in near future.