Connected and automated vehicles (CAVs) have been recognized as providing unprecedented opportunities for substantial fuel economy improvement through CAV-based vehicle speed trajectory optimization (eco-driving). At the same time, the implications of the CAV operation on thermal responses, including those of engine and exhaust aftertreatment system, have not been fully investigated. To this end, firstly, a sequential optimization framework for vehicle speed trajectory planning and powertrain control in hybrid electric CAVs is proposed in this paper. Next, the impact of eco-driving and power split optimization on the engine and catalytic converter thermal responses, as well as on the tailpipe emissions is characterized. Despite an average 16% improvement in fuel economy through sequential optimization, this study shows that eco-driving slows down the thermal responses, which could unfavorably affect the tailpipe emissions.