From what you're saying the Crosstar takes considerably longer, if at all, because the engine keeps cutting out ?
What happens depends on the driving conditions. First there's the warm-up problem. Initially the engine has some load until the battery is fully charged (turning on the heated seats will slow that charge rate down slightly) but once the battery is charged and the engine is running only to heat the cabin then all the extra efficiency due to the hybrid system is lost. If the vehicle is moving then there's a cold breeze through the engine compartment delaying the engine reaching the optimum operating temperature so it's below the potential best efficiency. At low to moderate speeds the engine should keep cutting out for the hybrid system to run efficiently but if the engine cuts out then it starts to cool down and the greater the ventilation through the engine compartment then the faster that happens. At higher speeds the engine is likely to be running continuously with more load on it so it's likely to warm up faster but until it's hot the mixture will be richer with more fuel going down the exhaust pipe.
Honda put grille shutters on the CR-V
https://hondanews.eu/gb/en/cars/media/pressreleases/159200/2019-honda-cr-v-hybrid56 . They know there's a problem needing to be addressed:
"Air inlets at the front, beneath the chrome Honda badge on the nose, feature Honda’s Active Shutter Grille system to improve fuel efficiency. By default, the system keeps the grille shutters closed as much as possible, even in city driving, to improve the aerodynamic performance. However, when required, the system operates an electronic step motor to open the grille shutters as much as necessary to allow airflow into the engine bay. A central processor tracks major temperature parameters for engine coolant, transmission oil and air-conditioning requirements, to determine the ideal state for the shutters."