Physics in my cup of tea

According to ohms law when resistance increase for constant voltage current will be decrease. And by joules law heat is directly proportional to current So heat also decreases with decreasing current value.

As the resistance increases the current decreases. But the voltage is constant. So, according to Joule's Law heat produced being proportional to voltage*current*time of flow of current and voltage and time being constant for comparison between the two cases, the current is lower when resistance is higher, so that the heat produced is lesser, or decreases with time.

The rate of heating depends on the power of the heater,

$P=IV\dots(1)$

Use Ohm's law $I=\frac{V}{R}$ to rewrite equation (1) as

$P=\frac{V^2}{R}$

So if the resistance is increased (while the voltage remains the same), the power is reduced, and so the tea will heat up more slowly.