Rhodes Island it's never very busy when it comes to traffic conditions, even in the High season when the island is full of guests the only very busy area is the city of Rhodes.
If you Drive South towards Lindos there's no problem even in the very busy months.
On the west side of the island, the only busy area is the area around the airport of Rhodes.
So no matter what time of the year you will be visiting Rhodes island, the rental of a car is the best and most comfortable way to explore it.