Problem with sending a POST request using the WiFiEsp library
Your problem is the content you are sending. While this format works well e. g. in Python libraries, this library seems to have a problem with it. 
I solved it this way, when I happened to face this problem: 

//all your other code, including the remaining HTTP-Request
String content = "{\"temperature\":\""+String(value)+"\"}";
client.println("Content-Length: 16"); //insert, well, your content length
client.println(content);