Does it make sense to speak of a temperature at the Big Bang?

Before the Big Bang, it doesn't make much sense to speak about anything with any certainty. This is because we don't think the concept of time as we know it today was a particularly useful concept to organize the various states of matter and energy.

But just after the Big Bang, when time and space became 'real', you can speak meaningfully about the amount of energy locked up in the curvature of space. Because temperature measures the amount of 'thermal' energy a system has, in this context you can relate the energy locked up in the curvature of space to an equal amount of energy available for pushing particles around if you have a mechanism for creating particles in the first place.

The limiting temperature for the Big Bang according to fledgling quantum gravity theory is about 10^32 K which is equivalent to 10^19 GeV of energy or the equivalent of 0.00001 grams converted into energy for each particle.