The part of the sentence "please accept my warmest wishes" is correct and usable in written English. You can use it in situations where you are expressing kind regards or best wishes. For example: "Please accept my warmest wishes for a successful job interview.".
"In conclusion, please accept my best wishes for your family".
Please accept my best holiday wishes for you and your loved ones.
Please accept my Valentine wish for more neighborly relations".
Choose to write something like "thinking of you in sympathy" or "please accept my condolences" if you wish to keep the note on the short side.
Please accept my regrets and apologies, also my best wishes.
Please accept my apology.
Once again please accept my sincerest apologies.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union