Equilibrium temperature of closed system

Body X of temperature 0° C is brought into thermal contact with body Y of temperature 100° C. X has specific heat capacity higher than of Y. The masses of X and Y are equal.

By my reasoning, the final equilibrium temperature should lie between 0° C and 50° C. Is this correct?

Edit: 1) The bodies are in thermal contact only with one another; they are in a closed system.

2) My reasoning:

${Q}_{x}={m}_{x}{c}_{x}\mathrm{\Delta}{T}_{x}$

${Q}_{y}={m}_{y}{c}_{y}\mathrm{\Delta}{T}_{y}$

${Q}_{x}={Q}_{y}$, ${m}_{x}={m}_{y}$

${c}_{x}\mathrm{\Delta}{T}_{x}={c}_{y}\mathrm{\Delta}{T}_{y}$

If ${c}_{x}$ is higher than ${x}_{y}$, then $\mathrm{\Delta}{T}_{x}$ must be lower thab $\mathrm{\Delta}{T}_{y}$, so the equilibrium temperature must lie below 50° C.