In this paper, we propose a convex planning model of integrated heat and electricity systems considering variable mass flow rates. The main challenge comes from the non-convexity of the bilinear terms in the district heating network, i.e., the product of mass flow rate and nodal temperature. To resolve this issue, we first reformulate the district heating network model through equivalent transformation and variable substitution. It shows that the reformulated model has only one set of nonconvex constraints with reduced bilinear terms and the others are linear constraints. Such a reformulation not only guarantees the optimality but fastens the solving process. To relax the remaining bilinear constraints, we apply McCormick envelopes and further propose a heuristic tightening method to constrict the bounds of the McCormick approach and get a nearby feasible solution. Case studies show that the tightening McCormick method quickly solves the heat-electricity planning problem with acceptable feasibility check and optimality.