Heating control more than half nibbled by the rodent (10)
I believe the answer is:
thermostat
'heating control' is the definition.
'more than half nibbled by the rodent' is the wordplay.
'more than half' becomes 'most'.
'nibbled by' is an insertion indicator.
'rodent' becomes 'rat' (rat is a kind of rodent).
'the'+'rat'='therat'
'most' put within 'therat' is 'THERMOSTAT'.
(Other definitions for thermostat that I've seen before include "Form of control" , "Heating device" , "Temperature controller" , "Temperature regulator" .)