The literature on team cooperation has neglected the effects of relative kindness intention on cooperation, which we measure by comparing the kindness intentions of an agent to her group members to the kindness shown by other members to this same agent. We argue that the agent's emotional reaction to material payoff inequity is not constant, but rather affected by her relative kindness intention. Then, we apply the model to team projects with multiple partners and investigate how inequity-aversion and relative kindness intention jointly influence team cooperation. We first consider the case of homogeneous agents, where their marginal productivity levels and technical capacities are the same, and then consider the case of heterogeneous agents, where their marginal productivity levels and technical capacities are not the same. Our results show that inequity-aversion has no effect on effort expenditure in the former case, but does affect it in the latter case. The consideration of relative kindness intention may impact the agents' optimal cooperative effort expenditure when their technical capacities are different. In addition, it is beneficial for team cooperation, and might not only reduce the negative impact but also enhance the positive impact of inequity-aversion on the agents' effort expenditures.