In the production of oil and gas in deep waters, the flow of the produced hydrocarbon through pipelines is a challenging problem. High hydrostatic pressures and low seabed temperatures may result in the formation of solid deposits, which in critical operating conditions like unplanned shutdowns can cause pipeline blockages. One of the possible methods for flow assurance, which can be jointly used with other approaches, is to heat the pipeline. This design concept aims at heating the produced fluid, if needed, to above a safe reference temperature in order to avoid the formation of solid deposits. The objective of this article is to utilize the particle filter method for the solution of a state estimation problem, in which the state variables are considered as the transient temperatures within a pipeline cross section. In addition, the minimum temperature in the region, predicted with the particle filter method, is used in the optimal control theory as a design tool for a typical heating system, during simulated shutdown conditions. An application example is presented to illustrate the control of the minimum temperature in the region, from an observer based on the particle filter method, where temperature measurements are assumed to be available on the external surface of the pipeline.