This invention relates to tires which have a rubber insert within the tire sidewall of a rubber composition which contains at least one of N,Nnull-(m-phenylene) bis citraconamic acid and N,Nnull-(m-xylylene) bis citraconamic acid. Such rubber insert is preferably of a stiff rubber composition which helps to support the weight of the vehicle to which the tire is mounted in situations where there is a loss of air pressure within the tire cavity. During periods of operation after loss of air pressure, the rubber insert is intended to aid in supporting a significant amount of the load assumed by the tire which leads to an internal generation of heat with the insert rubber composition, with an accompanying rise of temperature of the insert itself It is therefore important that the rubber composition of such rubber insert have a high degree of heat durability under conditions of working at the elevated temperature.