Does the cell internal temperature changes in response to a change in external temperature?
Homeothermic multicellular organisms have special tissues that burn resources to warm up (usually this involves breaking the electron-transporting chain at the final stages of respiration to transform all chemical energy into thermal energy). And they have special tissues (fat) and enough body mass (this is more about the volume/area ratio) to keep this energy from dissipating. If you recall physics, any unicellular organism has insufficient body mass to accumulate thermal energy for any perceptible amount of time, hence it's useless to burn resources that it can spend to adapt to lower temperatures, i.e. synthesise cold-shock proteins, modify membranes, restructure metabolism. This is basically the same reason why small mammals and birds have to eat all the time to stay alive. 



As you can see, the smaller you get the more energy you need to burn (hence increase ${O}_{2}$ consumption) to maintain body temperature. That's why we don't see truly homeothermic insects (some of them can warm up for short periods of time) or other small animals.