Answer:
The temperature of the methanol will increase more rapidly.
Step-by-step explanation:
The premise of your question is incorrect. Methanol has an OH group, so there ARE hydrogen bonds among methanol molecules.
However, the specific heat capacity of methanol is 2.53 J°C⁻¹g⁻¹, while that of water is 4.18 J°C⁻¹g⁻¹.
Thus, it takes 65 % more heat energy to raise the temperature of a given mass of water by 1 °C than it does to raise the temperature of an equal mass of methanol by the same amount.
The two samples are receiving heat energy at the same rate, so the methanol will heat up faster than the water.