Boiling/melting points of cyclohexane and cycloheptane
There are not many reputable sources on the matter (as I could find) since it seems that cycloheptane isn't the most popular chemical around (poor guy) but I will present you with the best explanation/argument/insight into the situation as I can. 

Note that it would be solely my own interpretation, and a case of explaining results that we see, rather than formulating an explanation to encompass natural phenomena without observing the results prior.

The key ingredient that I noticed while looking through charts and whatnot was bonding which is connected to sterics. More on that later.

Melting and Boiling Points of Cycloalkanes

Above is a chart of the melting and boiling points of cycloalkanes. As expected, boiling point increases linearly. That is lovely! Thus, we can explain boiling point with natural intuition, similar to regular alkanes. More is more! If only life was so simple.

Now let's take a look at melting points. HOLY! Cyclobutane? Why you so high? (it is actually an error by the book. Nonetheless, it is higher by a little than cyclopentane and that is the point) And wow, is cyclohexane a monster, past the melting point of our dearest water. Something is wrong with this universe. It must be the martians.

But no. It is not the martians. At least I do not believe so. The answer, I believe, is sterics.

Sterics? you ask. Are you trying to say that cyclobutane bonds more structured than cyclopentane and cyclohexane bonds more structured than cyclohexane?

Precisely.

Although you may not expect much difference from cyclobutane and cyclopentane, cyclobutane is very close to a right angle (perfect square) and this would allow tight packing. Cyclopentane, on the other hand, is normally as an "envelope" which allows less close packing.

Similarly, cyclohexane has  very close cystalline packing which may account for its low melting point. 

Then, after its crystalline structure melts away, our intuition gives way to the boiling point expectancies.

Again, this is not definite. If possible, I would like to juxtapose the solid structures of each cycloalkane, but unfortunately data seems scarce, especially for cycloheptane, which is of concern.