Can there be a time-temperature graph as follows?

No, there cannot be a time-temperature graph as shown. A time-temperature graph shows the relationship between time and temperature. The graph implies that the temperature changes instantaneously, which is physically impossible for most real-world systems. Temperature changes require energy transfer, and this transfer takes time. An instantaneous change in temperature would require infinite power, which is not physically achievable. Therefore, a realistic time-temperature graph would show a gradual change in temperature, not the abrupt jumps depicted in the hypothetical graph. The rate of temperature change is governed by factors like heat capacity, thermal conductivity, and the rate of heat transfer.