Is there a bluetooth thermometer with a button that sends the temperature as keyboard input?

I have a web app that asks the user to type in the temperature of something. I'd like to find a thermometer (ideally for food) that shows the temp and, at the press of a button on the device, sends the temperature value to the phone/tablet as if it were an external keyboard. (The page doesn't care if the user types in a value or sends it from the thermometer.) I don't care about continuous data collection and think this approach would simplify the process.

I've spent an hour looking for something like this to no avail.

Is anyone aware of a device that works this way? Is there a flaw in my thinking above?