Lincolnshrie Police say they are investigating the thefts in Woodhall Spa and Corby Glen, Grantham.
Both Lincolnshire and Humberside fire services have warned about being careful near frozen lakes.
Brant Broughton, Billinghay and Metheringham stations were targeted last week, say police.
Esme Baker and her father Lee Baker died in a caravan fire in Ingoldmells in April.
A sleigh will visit Lincolnshire towns during December to raise money for the Fire Fighters Charity.
Lincolnshire Fire and Rescue say they are struggling to recruit and retain on-call firefighters.
The devices combine a light and fan and could pose a fire or electric shock risk says Ashley Waines.
Lincolnshire Fire and Rescue says it has seen a "sharp increase" in calls to wildfires this year.
Lincolnshire Fire and Rescue was called to the house in St Mary's Lane, Louth, just after 10:00 BST.
