In the UK, the most common make of thermostats is Habistat. That is your urgent priority! With no thermostat, there is nothing to tell you if it stops working and the snake gets cold... or much worse still... with no thermostat... there is nothing to prevent a fault where it heats up so hot it cooks the snake... which is, unfortunately a common fault in heatmats.
Long term, you would probably be much better off looking into getting a ceramic heat lamp and a stat, heatmats are just... *meh* if its a big ole snake, it will get hot very quickly sitting on a heatmat and they are often too stupid to get off the heatmat. With a ceramic bulb, you can set it (with a guard) down one end of the vivarium which will give you better control for the temperature variant down each end of the vivarium.
As for the frozen/thawed food, that is the best way to go, corn snakes are rarely ever fussy feeders! But some snakes do dislike wet food, found a good way of defrosting it and keeping it dry is using a hair dryer
or if you get the ceramic on the viv, keep the heatmat and lay frozen mouse on the heatmat to defrost.
He will definitely want an adult mouse or a really small rat at the size he is but depending on how fat he is, might only want feeding every 10 days or so....
My friend has a good website, a good simple article on corns as well...
http
/www.thamesvalleyexotics.co.uk/page6.htm
Here is the heating you want:
Pulse Stat
http
/www.eurorep.co.uk/heating/thermostats/habistat-pulse-prop-thermostat
Ceramic (though I am not sure on wattage..)
http
/www.eurorep.co.uk/heating/ceramic-heaters
If you are on FB, ask Kat on here for any questions or photos of her corn snake setups, she will most happily oblige
https
/www.facebook.com/pages/Thames-Valley-Exotics/203422953746?fref=ts
Here is my corn (had to sell her when I moved in with my now ex), she was a beautiful American bred Serpenco Butter corn snake called Flora lol.