No need for a fancy thermometer
Just buy a regular plain one from the drug store and use it under the armpit. I recommend against doing rectal temps unless you know what you're doing. Granted, it's true that it's not that hard, but it could be inserted to far, or at the wrong angle, or the baby might move out of your grip, and you might end up doing some damage accidentally. At my hospital, we only check rectally once, and that's just to make sure everything's open down there. Afterwards, we only do armpit temps (and they're nearly as accurate).