TL;DR : There's no reason for it to show any periodicity. It doesn't depend in a simple way on the outer electron configuration of atoms. The specifics of crystal structure are important in ferrmoganetic (also in antiferromagnetic, and ferrimagnetic) materials.
This by no means is a complete description of the phenomenon. If you're interested, consult textbooks, the internet etcetera. and come back with more specific questions. The person who originally asked the question seemed like he was a high school student (or lower) so I tried to tailor an explanation that he would understand. I welcome more complete desscriptions
First of all, ferromagnetism is a property that goes beyond the chemistry of a material, and is highly dependant on crystalline structure and microstructure.
Existence of several ferromagnetic metal alloys whose constituents are not themselves ferromagnetic (Heusler alloys), and conversely, the existence non-magnetic alloys, composed almost exclusively of ferromagnetic metals (for example some types of steel) are evidence of this fact.
The OP originally spoke of unpaired electrons, so I am guessing he knew something about electron spin.
Spin, just like electron charge is an intrinsic property, and its behaviour is described using quantum mechanics. Spin and charge on the electron give rise to a magnetic dipole moment (people like to talk about classical charges spinning and generating a magnetic dipole, however, I would like to discourage this analogy).
Due to its quantum nature, the spin of the electron can be in one of only two states; with the magnetic field either pointing "up" or "down" (what I call up and down is somewhat arbitrary; what's important here is that there are two arbitrary, mutually exclusive eigenstates).
The spin of the electrons in atoms is the main source of ferromagnetism, although there is also a contribution from the orbital angular momentum of the electron about the nucleus.
Materials made of atoms with filled electron shells have a total dipole moment of zero, because the electrons all exist in pairs with opposite spin, every electron's magnetic moment is cancelled by the opposite moment of the second electron in the pair.
So of course, a ferromagnetic material needs to have spin unpaired electrons, but that alone isn't sufficient. Hund's rules, posit that the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment.
These unpaired dipoles (often called simply "spins" even though they also generally include angular momentum) tend to align in parallel to an external magnetic field, an effect called paramagnetism. Such materials are hence called paramagnetic. Molecules with spin paired electrons are called diamagnetic.
Ferromagnetism involves something extra. In a few substances the dipoles tend to align spontaneously, giving rise to a spontaneous magnetisation, even when there is no applied field. This is ferromagnetism.
Now let's develop some specifics. For instance, how and why do spins align? Additionally, why can we find iron in both magnetised and unmagnetised states, shouldn't it always be magnetised?
When two nearby atoms have unpaired electrons, whether the electron spins are parallel or antiparallel affects whether the electrons can share the same orbit as a result of the quantum mechanical effect called the exchange interaction. The exchange interaction is related to the Pauli exclusion principle, which says that two electrons with the same spin cannot also have the same "position".
When the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, electrostatic repulsions are reduced when spins are parallel to each other. In simple terms, the electrons, which repel one another, can move "further apart" by aligning their spins, so the spins of these electrons tend to line up. This difference in energy is called the exchange energy. In ferromagnetic materials, the exchange interaction is much stronger than the competing dipole-dipole interaction. For example, in iron (Fe) the exchange force is about 1000 times stronger than the dipole interaction.
Therefore, below the Curie temperature virtually all of the dipoles in a ferromagnetic material will be aligned. (we will get to Curie temperature in a minute)
So why are iron and other ferromagnets ever found in an "unmagnetised" state ?
The reason for this is that a bulk piece of ferromagnetic material is divided into tiny regions called magnetic domains. Ferromagnetic materials spontaneously divide into magnetic domains because the exchange interaction is a short-range force, and over long distances of many atoms the tendency of the magnetic dipoles to reduce their energy by orienting in opposite directions wins.
If all the dipoles in a piece of ferromagnetic material are aligned parallel, the space surrounding it contains a lot of magnetostatic energy, which the material wishes to reduce, and it does so energy by splitting into many domains pointing in different directions, so the magnetic field is confined to small local fields in the material, reducing the volume of the field.
This means that within each domain, the spins are aligned, but (if the bulk material is in its lowest energy configuration, i.e. unmagnetised), the spins of separate domains point in different directions and their magnetic fields cancel out, so the object has no net large scale magnetic field.
The domains are separated by thin domain walls a number of molecules thick, in which the direction of magnetisation of the dipoles rotates smoothly from one domain's direction to the other
Although the exchange interaction keeps spins aligned, it does not align them in a particular direction. Without magnetic anisotropy, the spins in a magnet randomly change direction in response to thermal fluctuations and the magnet is super-paramagnetic. There are several kinds of magnetic anisotropy, however, let's not go into that here
If one now places such a material in a strong enough external magnetic field, the domains will reorient so more of the dipoles are aligned with the external field. Moreover, the domains will remain aligned when the external field is removed, creating a magnetic field of their own extending into the space around the material, thus creating a "permanent" magnet.
The domains do not spontaneously return to the original minimum energy configuration when the field is removed because the domain walls tend to become fixed in place by the crystal structure, and defects in the bulk solid. Thus the magnetisation, and the resulting magnetic field, is baked into to the crystal structure of the material, making it very difficult to demagnetise (it is metastable in this sense).
As the temperature increases, thermal motion, competes with the ferromagnetic tendency for dipoles to align, and when the temperature rises beyond a certain point, (the Curie temperature), the system can no longer maintain a spontaneous magnetisation, as reorientation takes place.
This is an example of a second order phase transition
Thus the material looses its ferromagnetism; unpaired electrons are still present, and thus it is still paramagnetic.
Now clearly, you can see that ferromagnetic properties don't depend in a simple way on unpaired spins, and there is no reason for the curie temperature to follow a periodic trend the way you expect it to.