I think that recipes should replace phrases like medium high heat or simmer with temperatures. I interpret medium high heat to mean about 350-370 degrees Fahrenheit (175-190 C). Likewise, I call a simmer about 200 degrees (about 95 C).

For measuring pan tempuratures, I use a point and shoot infrared thermometer like this model on Amazon: https://www.amazon.com/dp/B00DMI632G/.