There is definitely no shortages of gear on the market for keeping warm in a hammock. To answer the question you really must understand where you are going and how much money you have to spend.
Determine the climate and temperatures you plan on hanging. If you are doing a backpacking trip in the fall or winter you want to be prepared if the temps suddenly drop.
I will discuss 3 basic types of insulation, which can be used for hammocks:
1) CCF (closed cell foam) pads
A single bottom has one layer of material on the bottom of the hammock. This can help conserve weight. However, it's not ideal if you plan to use a slippery pad under your back for insulation.
A double bottom hammock has two layers of material on the bottom which are sewn together like a pocket. The space between the two layers is where you want to put your insulation if you are using an air or a CCF pad.
The purpose of the double bottom is to help keep the pad in place and prevent it from shifting. A shifting pad can be extremely annoying when trying to sleep, especially in colder temperatures. It still takes a little practice to properly adjust your pad.
Both types of pads are great if there is any risk of having to go to ground during your trip. This can be common at higher elevations and areas where there isn't any trees or places to hang a hammock. Fortunately most hammocks can easily be setup on the ground similar to a solo-tent or bivy. This is where the use of pads really shine.
CCF pads are generally lighter than air pads, but are usually not nearly as comfortable. The true purpose for a CCF is to keep you insulated from the ground so you stay warm.
Air pads on the other hand keep you insulated with the added benefit of comfort. They are more costly than CCF pads but well worth the extra money in my opinion.
CCF and air pads work similarly in a hammock as they do on the ground. CCF pads may be more comfy in a hammock, however. This is because you don't have to worry about rocks, and such, sticking in your back. There is nothing worse than sleeping in that one lumpy spot you cannot fix.
One common issue with pads in a hammock is they tend to curve around your body leaving your shoulders and hips exposed to cold spots. Wider pads can work, but tend to fold which can cause some discomfort. Some companies make special attachments for your pads to get around these issues.
My preference is to use an under quilt. Under quilts connect to the bottom of a hammock and when adjusted properly provide superior warmth. They are very light weight as well. There are both down and synthetic quilts for your hammock.
The downside to quilts is they cannot be used if you need to setup your hammock on the ground if you don't have trees. Some people carry small pads in addition to quilts if they are in areas where trees may be an issue.
In all honesty it all comes down to purpose and personal choice. For me I usually only carry my quilt unless I think there may be an issue with trees then I bring and air pad, or a CCF pad + quilt.
Keep in mind, even if you have an under quilt you will still need a top quilt, or a blanket of some sort. I like down top quilts because they are very light weight. The downside is if they get soaked they won't insulate. Synthetic will keep you warm even if its wet.
There are quilts that wrap around your hammock, but the drawback is you cannot use a hammock which has a built in bugnet, or weather shield.
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