Definitely! The volume that a given amount of air takes up depends on its temperature. Since the amount of air in a balloon is fixed, if you change its temperature its volume must change, and so must its size. So yeah: if you heat up a balloon, its circumference will get bigger, and if you cool it down, it'll get smaller.

A balloon is an elastic body filled with gas. To a first approximation, the gas (usually air) in the balloon can be modeled as an ideal gas (this model assumes that the atoms or molecules with in the gas do not interact with each other). The ideal gas equation relates the Pressure (P), Volume (V), amount (n usually measured in moles), and Temperature (T measured on an absolute scale in Kelvin) to the gas law constant R in the following manner:

If you blow up a balloon and tie it off, you have enclosed some amount of gas (n) at some pressure (Pi), volume (Vi), and Temperature (Ti) such that:

(Pi*Vi)/(n*Ti)=R.

If you now heat the gas up (Tf is greater than Ti), the new pressure (Pf) and volume (Vf) can be related to the gas constant as:

(Pf*Vf)/(n*Tf)=R

where n is the same since the balloon is tied off and you did not change the amount of gas inside the balloon. Now, the gas constant is just a number and does not change so you can equate the two equations as:

(Pi*Vi)/(n*Ti)= (Pf*Vf)/(n*Tf)

which can be rearranged by algebra to give:
(Pi*Vi)/(Pf*Vf)=Ti/Tf

and the n drops out because n/n=1.

Since Ti is less than Tf,then that means Pi*Vi is less than Pf*Vf.

Now, since we know that as the pressure increases, so too must the volume (in other words, when you blow up a balloon (increase the pressure), the balloon gets bigger (volume increases), we then know that Pi is less than Pf and Vi is less than Vf.

Since the volume of the balloon is getting bigger (Vf is less thanVi) then we know that the balloon must have expanded meaning that the circumference of the balloon must also have increased. In summary: as you heat a gas, it expands. In a balloon, this expansion would increase the circumference of the balloon. Also, by the same logic the reverse is true: as you cool a gas, it contracts. In a balloon, cooling the gas inside would cause the circumference to decrease.

If a balloon is heated up, the gas inside will expand, causing the circumference of the balloon to increase. Similarly, if the balloon is cooled down, the gas inside contracts, and causes the balloon to shrink.

Short answer: Yes.

Long answer: Because a balloon is filled with a gas instead of nothing, the gas can contract or expand due to temperature. Think of it as a class of students, who have lots of energy - they probably want to run around in a large space instead of a small space. On the other hand, a class of students who have very little energy will be able to sit quietly together, like at reading time. This contraction of the students takes up less room, just like a cold gas in a balloon.