Power calculation in kwh over a period of time with a variable current source
Power is measured in watts (W).
Electrical energy is measured in watt-hours (Wh).


Your understanding of P = VI is correct and will be in watts. That gives you the power. Since your interval of measurement is one hour the watt-hours will be the same numerical value.

Assuming the power rises or falls continuously during the experiment (rather than randomly increasing and decreasing) I would use the average power for the interval: \$ P_{n} =  \frac {P_{n-1} + P_n}{2} \$ where \$n\$ is the measurement number.