A Mintemp error happens when your thermistor for one of the hotends is reading 0C or below. This is usually the result of a break in the thermistor wiring, it can also be due to the toolhead not being plugged in or if you are using a dual extruder it can be because the two wiring harnesses for your toolhead got switched around.
Thermal Runaway is triggered by the primary hotend dropping in temperature beyond a threshhold set in the firmware. It can be caused by a failing heater cartridge or excessive fan on the hotend, or in a worst case scenario, by the thermistor coming out of the toolhead during printing.
Since you have experienced both a thermal runaway and Mintemp error I would suspect something is going wrong with your thermistor. If you have access to a digital multimeter, you can check the resistance measurements on the tool head to see if the thermistor or heater cartridge is bad. With the printer turned off and unplugged, disconnect the hot end from the wiring harness and test hot end for the proper resistance. The smaller black and red wires coming from the hot end are for the thermistor and should read ~100k ohms at room temperature. The larger red wires are connected to the heater cartridge and should read ~20 ohms.
