The mat will be fine to maintain the temperature on the floor of the tank, which is where the snake is. Don't worry about ambient air temperatures - the snake isn't hovering in mid-air.
Don't worry about the winter. It won't get to minus 10 inside the house, otherwise you'd get frostbite! Generally, if the room temp is warm enough for a human to be reasonably comfortable, then the cool side of the Corn's tank will be fine. The lower end of the temp scale isn't as crucial as the high end (lower than ideal and they just slow down, too high and they can die). I didn't switch my central heating on until December and my Corns are in the lounge. They ate/digested/pooped normally throughout and showed no unusual behaviour.
You really need to get a stat for the mat so that you can be sure what temp it is. You also need to get a digital thermometer to meaure the floor temp, rather than a strip or dial-type, if you haven't already. The strip/dial ones are notoriously inaccurate.