Off the top of my head, a used iHome ISS50 (eBay) would do the job. Or a HomePod mini. Both are always-on, WiFi-enabled, HomeKit-compatible temperature and humidity sensors.
As far as checking and reporting to an app, though... That I'm not sure about. You can set up automations/alerts in HomeKit, or do temp checks at times of day and do something with the result (like make a light glow red or something)