how to use ESP 8266 to transfer data to a web page ?

here is a prototype of mine, a clock and weather station for my amateur astronomy observatory. It transfers the temperature to my website every minute, calling an API endpoint via HTTPS, itself being connected to my local wifi.

So it is not filling in a form on a rendered page or something. It calls an endpoint via the same protocol websites are being called into the browser (see also http verbs Hypertext Transfer Protocol