The temperature increases rapidly after
a. Troposphere
b. Exosphere
c. Ionosphered. Stratosphere

Temperature rise in Ionosphere has the following reason:
The density of the gases goes very very low here. The pressures are also very low, just a few millipascals away from the total vacuum. Hence, the collisions are very rare. Mean free path will be very high. Collisions do not average the temperatures like what happens in the lower levels of the atmosphere. So, if you keep a thermometer, some molecular collision may indicate a temperature as hot as 10000 K, and sometimes as low as 10 K. The temperature is not measurable here. Because temperature, by definition is the measure of the average kinetic energy of the colliding molecules in contact. The temperature here is not, in a strict sense "measured", it is rather estimated based on the energies of the molecules in this region.