We present an algorithm for testing flexibility [as defined by Cerda et al. Computers chem. Engng 14, 197-211 (1990)] at the level of heat matches in the design of heat exchanger networks, when inlet temperature variations are allowed under certain restrictions. Following this definition, we say that a heat exchanger network (HEN) is structurally flexible for a given range of variation of parameters, if it guarantees operability (feasibility) and maximum energy recovery between process streams. In the design of such a network, it is convenient to divide the network into substreams according to the inlet temperatures of the process streams, giving rise to a transportation network to which our test may be applied. In this paper we do not consider HENs in which there are forbidden matches and/or several utilities (with different operational costs or levels), although we believe that our technique could be extended to these cases with suitable modifications. This is so since we make explicit use of the simple network "cuts" available in the HENs we consider (essentially Linnhoffs "pinch"). More general networks will need a more general form of the corresponding cuts, and therefore are not as simply handled. The test we present is a mixed integer linear program (MILP) which considers the whole set of operation points at once. We should emphasize that it does not give optimality (for example, of minimum number of units) but just flexibility. Thus, the test could be embedded in a synthesis procedure, for instance it could be used in the first stage of the two-stage procedure described by Floudas and Grossmann [Computers chem. Engng 11, 319-336 (1987)]. In this regard, we should mention that the test in that paper does not test for flexibility (as discussed in this paper) but rather feasibility, as we show with an example. Thus, although the temperature range we consider is convex (a "rectangular" region), it is not enough to test the extremal points (vertices) for flexibility. Hoping to tackle flowrate variations in a separate paper, in this work we consider only temperature variations. Moreover, due to the complexity of the general case, we present here the case where the different temperature ranges do not overlap (as will be described with more precision in the sequel). The proposed MILP was tested on several examples and the performance on these indicates that the test might not be a too "hard" MILP, according to the number of branches in the procedure.