20x10 is a pretty reasonable size. My thermo came from home depot, it is not bluetooth but it was cheap < $20 and has good wireless range, no alarm though. I'm sure they have some that connect to your phone and/or have an alarm, but they'll cost more.
The smaller the greenhouse, the harder it is to prevent from overheating. I don't use an app, but I have a remote thermometer that I can read from inside the house. I have a fan going during the warmest part of the day for circulation, in addition to opening the door/vents.