Monde and Mitsutake [1] recently proposed a new idea for immersion cooling that the quench starts when the surface heat flux q(t) during the immersion cooling reaches exactly the critical heat flux qc at a critical time tc* depending on a couple of solid and liquid. This time tc* during immersion cooling of liquid nitrogen (LN2) appears tc* = 1.4 ~ 2.4 ms for some rare sphere solids. Monde and Mitsutake [2] expand their idea for the immersion cooling of Al sphere coated by a thin Teflon film and explain the reason that the temperature at which its quench occurs, shifts to higher temperature with increase in the thickness of Teflon. This study firstly focuses on the short period of time immediately after the immersion of a cylinder coated by thin film into a liquid and then derives an exact solution for the temperature during the immersion cooling. It reveals for about 10 ms after a contact of the Cu cylinder coated by Stycast with liquid Nitrogen(LN2) that the temperature for the cylinder is uniformly kept at a constant temperature, while the surface temperature on Stycast contact with LN2 drops at a moment of their contact until a certain temperature which is determined by both initial temperatures of the cylinder and LN2 before their contact and then the temperature in Stycast film largely changes with time. In addition, the quench starts within the time of tc* = 10 ms, after the immersion of the Cu cylinder coated by Stycast into LN2.The mechanism that the coated film makes the temperature, at which the quench starts, higher, is clearly explained.