To some degree the fuel can be recycled, the process is called reprocessing.

The easiest form of reprocessing is to chemically separate the plutonium that the reactor produced during its operation. This plutonium is then mixed with fresh enriched uranium to produce mixed oxide fuel (MOX) for use in reactors, cutting down the demand for expensive enrichment. This still leaves the spent uranium and fission products and all the transuranic (other than plutonium) in the radioactive waste, as well as producing significant amounts of liquid chemical wastes containing radioactive contaminates. France is the only country that uses this process to any degree at this time.

A better form of reprocessing uses an electroplating process to separate uranium and all the transuranic (not just plutonium) that the reactor produced during its operation. This only leaves the fission products in the radioactive waste. No country currently uses this process, but the US tested it while they were developing the integral fast breeder reactor (which got canceled before a complete prototype could be built).

Your question expresses a significant bit of conceptual confusion. Perhaps I can clear up some of this confusion and at the same time answer your question.

What we call temperature is simply the manifestation of kinetic energy at the level of the atom (i.e. slow moving atoms = low temperature, fast moving atoms = high temperature). What we call nuclear energy is simply an excess in the nuclear binding energy, which is the energy binding the protons and neutrons together inside the nucleus and is a manifestation of the strong nuclear force and to a lesser extent the weak nuclear force. This movement of atoms has no affect at all on whether there is or is not excess nuclear energy inside atomic nuclei or if that excess nuclear energy is being released or even can be released. Those nuclei having the least nuclear binding energy are the nuclei of the elements from iron through lead, both the elements lighter than iron and the elements heavier than lead have more nuclear binding energy (which can be considered to be excess nuclear binding energy that could potentially be released).

There are three processes that can release excess nuclear energy: radioactive decay, nuclear fission, and nuclear fusion. All of these processes transform nuclear energy to kinetic energy at the level of the atom (i.e. temperature aka heat), and thereby convert a small amount of the mass of the atom into energy. Of these three both radioactive decay and nuclear fission can take place at any temperature, even those so cold as to approach absolute zero. Neither radioactive decay nor nuclear fission takes place any faster or slower with a change in temperature. Nuclear fusion though can only take place at very high temperatures (and pressures) as the nuclei must be very close together and moving fast enough to be able to collide and fuse, despite the strong electrostatic repulsion due to both nuclei involved being positively charged. But this is a threshold temperature, even at high temperatures just below the threshold no nuclear fusion can take place at all and once above the threshold and nuclear fusion begins, raising the temperature further has very little affect on the rate at which that nuclear fusion takes place.

Nuclear reactors operate using the process of nuclear fission and generate heat by both nuclear fission and radioactive decay. We are not yet able to extract nuclear energy in a controlled manner using the process of nuclear fusion (only explosive release of nuclear energy has ever been successfully done using the process of nuclear fusion).