Bought one of these for the wife and it seems to work fine. Has a ponytail hole and should cover the temples. Cheap enough to give it a whirl.
First - do NOT cycle without a helmet.
Secondly - skullcap. You can get them on Amazon for like $13. I have this one, it won't make you too hot or sweaty. https://www.amazon.com/gp/product/B00PVUR34K/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
Bonus: they help kill wind noise and can prevent tinnitus.
I have the same problem. The cat ears are an incredible waste of money, don't bother with them.
What has worked best for me is combining a cycling skull cap like this one
https://www.amazon.com/gp/product/B00PVUR34K/ref=ppx_yo_dt_b_asin_title_o09_s01?ie=UTF8&psc=1
With some comfortable wireless earbuds like the (excellent) Jabra 75T
https://www.jabra.com/bluetooth-headsets/jabra-elite-active-75t##100-99093004-15
You can enable hear-through on these which makes it easy to hear outside sounds while minimizing wind noise which is incredibly damaging and can cause hearing loss.
I use this under my helmet, it’s effective and cheap.
https://www.amazon.com/gp/product/B00PVUR34K/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
A cap with ear cover under 15 http://www.amazon.co.uk/gp/product/B00PVUR34K/ref=s9_hps_bw_g200_i3