In order to help you, we need a bit more information than you have provided. What type of plants? Where do you live? Are you talking about year 'round or thru a winter? Indoors or out? Size of the cold frame?
Any time you have a question its helpful to provide as much information as you can so everyone can get the picture of the situation.
Give us some more info and I'm sure someone can help you.
I also live in the UK and have grown venus flytraps and Sarracenia pitcher plants without heating even though we have hard frosts and snow. Keep them unheated, but with your hanging pitcher plant, you need to grow that in your home in a humid place eg in your bathroom (English version, not American!!
where it is likely to be more humid especially if you have a shower installed there.
Generally speaking, don't try the paraffin heating option at all, because of the fumes and the limited space you have. But your plants will appreciate the cold temperatures this winter to achieve the dormancy those particular plants require.