How can i fix my Boss BRTRF remote thermostat controller?

1) You've put them in wrong
2) Check the positive terminal on the new batteries isn't wider than the one on the old batteries.

I mention 2) as I had an issue with a battery powered gizmo some time ago, where the positive terminal in the gizmo was "protected" by a couple of raised plastic lugs.

New batteries had a wider positive terminal than the gizmo was expecting. Result: Battery positive terminal "sat " on the lugs and never touched the metal contact. Found some different batteries and used them - don't be tempted to trim the lugs; they are here to protect the device in the event you manage to put batteries in backwards.

HTH
October 2016