Is this problem still remaining now that you’ve moved the two units apart?
If it is, I think I’d suspect the emonTx first, and condensation. There’s very little power dissipated inside the case - which isn’t sealed owing to the need to connect to the p.c.b. - so there’s a greater likelihood of condensation occurring.
Even if you don’t have the problem any more, from what you’ve written about the conditions, I’d suggest you still think about putting a little heat into the emonTx.
One thought would be to use the a.c. adapter to supply some heat. It’s grossly overrated as far as supplying the electronics is concerned, and a bit of load would actually improve the quality of the waveform, even though it will affect the calibration - because the calibration is based on the no-load voltage being 11.6 V (if you’re in the UK), whereas at full load, it will be 9 V. The adapter is rated at 10 W, so you could think about a resistor dissipating about a watt connected directly to the a.c. input socket. 120 Ω would give a fraction over 1 W, a 2 W or 3 W resistor would fine, I wouldn’t use a 1 W one - that would run quite hot. Or you could use 2 × 220 Ω 1 W in parallel, or 3 × 330 Ω 1 W in parallel.
That would affect the calibration by about 10%, which you’d need to correct, either in the sketch itself or in the emonBase. The voltage and power will be reported that much lower than they really are.
I’d have thought that there’s probably enough heat within an emonBase - provided that the enclosure is reasonably closed but allows a little ventilation - to keep condensation at bay.
Without checking each individual component, I cannot say definitively but it would seem unlikely that the problem is temperature alone - unless it goes some way below 0 °C.
[Edit] I’ve checked the processor and the radio, and the likeliest passive component - an electrolytic capacitor, and that’s the worst, being rated down to only -40 °C. So again, without checking each component, the temperature in a UK unheated building isn’t likely to be the immediate problem.