The charts below are are showing the frequency reported by WSPR 2.11, which as I understand it will be the first frequency it decodes and the amout of drift from that frequency over the life of the transmission.
The amount of drift once the transmission begins is in the opposite direction and after some initial jitter assumes asymptotic behavior at a consistent 2 hertz downward drift as the device warms up.
While none of these figures is horrific, good engineering would indicate that for this kind of application, careful attention to thermal stability is important.