Does radioactive decay speed up at higher temperatures?

No.

Radioactivity is a function of the weak nuclear force which is not affected by temperature. The weak force acts within

the nucleus only, whereas things like temperature and pressure affect only

the electron cloud surrounding the nucleus.

At "ordinary" temperatures, it is true that temperature has no effect on radioactive decay rates. However, at temperatures at which the blackbody temperature of a material is high enough to produce photons that have energies that are comparable to nuclear excitations (i.e., "gamma-ray" photons in the many MeV energy range), these photons cause photonuclear reactions that alter the stability and overall decay rates of nuclei. That is, photons in the multi-MeV range can "reverse" the neutron capture reactions that are commonly occur between low-energy neutrons and nuclei. Instead of (n, gamma) reactions, at high energy one gets (gamma n) and (gamma, 2n) reactions). Such conditions are not found on Earth, but are common in stellar interiors.

Answerer Civil notes that "things like temperature and pressure affect only the electron cloud surrounding the nucleus". This is quite true. However, there is one mode of nuclear decay that *is* affected by the "chemical" state of the atom, and that is electron capture.

In electron capture, which is a form of beta decay, an atomic nucleus "captures" an atomic electron, with the net effect of converting a nuclear proton to a neutron. This process can occur because the atomic nucleus has a non-zero size, and the wavefunctions of the atomic electrons have nonzero values in the region of space occupied by the nucleus.

Any process or effect that increases the probability of an atomic electron being "in" the nucleus will increase the probability of an electron-capture decay. Therefore, higher pressures, or any chemical "state" that changes the "overlap" of the nuclear and electronic wavefunctions will change the decay rate of nuclei that decay via electron capture.

Changes in the electron-capture decay rate of Be-7 and Na-22 due to changes in external pressure or chemical state of the atoms have been observed, and are well documented.

No