Heavy cream is high in saturated fats consisting of long-chain fatty acids. Fat molecules usually consist of three strands of molecules called fatty acids, connected together to form one fat molecule. Fatty acids are long molecules, and the longer they are, the more easily your body changes them into cholesterol molecules. Most animal fats (with certain exceptions such as fish oils) are made of very long fatty acid molecules which have the maximum number of hydrogen atoms on them (thus they are called "saturated" fats). These long-chain saturated fatty acids are the easiest to convert into cholesterol, which when found in excessive amounts in the bloodstream, end up getting deposited in the lining of arteries throughout the body, eventually leading to narrowing and blockages in the arteries, leading to such health problems as heart attacks, strokes, and gangrene of the legs.
Most plant-derived oils are not fully saturated. The healthiest oils are called mono-unsaturated, meaning they only have room for one additional hydrogen molecule. Because of this, they are not so easily made into cholesterol by your body, and in fact can block your body's ability from making excess cholesterol from any saturated fats you might have eaten. Monounsaturated fats are found in olives/olive oil and avocados/avocado oil, as well as many nuts and nut oils such as walnuts, pecans, almonds, and even peanuts, to a lesser extent. Many other vegetable oils, such as corn oil, soybean oil and "canola" (rapeseed) oil are called poly-unsaturated, meaning that they have room for several additional hydrogen atoms. If extremely fresh, these oils are healthy, but because they have room for so many hydrogen atoms, that means that they spoil (called "going rancid") easily, unless stored carefully. Polyunsaturated fats do not necessarily smell bad when rancid, like saturated fats do (such as rancid butter), so it is hard to tell when a polyunsaturated oil has gone rancid. Rancid oils have been shown to cause generalized inflammation in the human body, especially within blood vessels, which can ironically lead to the same sort of blockages in arteries that excess cholesterol can. So you're not necessarily doing yourself a lot of good by using polyunsaturated vegetable oils in place of saturated fats like cream or butter.
The WORST types of oils are polyunsaturated vegetable oils which have been artificially hydrogenated, or "saturated", in order to make them solid at room temperature, such as Crisco or margarine. These are the so-called "trans-fats" you hear about in the press lately, and for good reason. They produce the highest levels of inflammation inside arterial walls of all types of fats.
There are naturally occurring saturated fats found in some plants, namely coconuts and palm-tree oils. Coconut oil especially has been found to consist of medium-chain fatty acids, which are too short for your body to easily convert into cholesterol, and some scientific studies suggest that coconut oil (which is solid at room temperature, like Crisco) can actually have an anti-inflammatory effect on your blood vessels, and might even protect against heart attacks and strokes like olive oil and fish oils do.
I am a physician with over 20 years of experience.