The signals from the Router may be swamping the wireless thermostat receiver but I doubt it - you can easily check by turning off all computers and pulling the power connection to the router - it the wireless thermostat then works switch the router back on and see if the wireless thermostat starts to play up again - a diagnosis.
I had never herard of wireless thermostats until recently and can't understand why anybody should want one - our room stat is hard-wired in the hall - we keep it set to 16 or 10 depending on if we want the boiler to run or not - TRVs keep the other rooms at the temerature we want. There are no communication issues with the boiler - not with a permanently wired thermostat.
I just can't imagine anybody needing to move the thermostat from one place to another - but I am an old fuddy duddy.
Having said all this my room stat did fail recently when we pulled down the hall ceiling - grit and dust got into it and the CH failed accordingly - I had to remove it from the wall and clean up the contacts - 10 mins work...
Good luck...
Peccavi
November 2009