I have built a little thermostat based on BMP280 temperature sensor over I2C, ESP8266 Lolin v3 and STX882 433Mhz transmitter.

I am not using pullups resistors or decoupling capacitors.

Everything works fine when the components are out of the enclosure (see picture), but when I put them inside the enclosure the BMP280 readings start to 'oscillate' as shown in this picture[![See the oscillation after 18:00. Ignore the spikes, that was me touching the sensor.][1]][1] 

I am not an electrical engineer and the only thing I can think of is that there is some kind of interference between the transmitter and the BMP280 or I2C bus.

To give you and idea I am also attaching two pictures of the thermostat.
[![Closed enclosure][2]][2]
[![Open enclosure][3]][3]

Any suggestion?

  [1]: https://i.sstatic.net/1RbVp.png
  [2]: https://i.sstatic.net/zMy2e.jpg
  [3]: https://i.sstatic.net/qMlUo.jpg