Yonks ago I bought a timer for an immersion. You had to wire the
immersion into the timer (like a CH timer), not plug it in.

I also ran some convector heaters from the equivalent plug-in
model (so old now it isn't worth mentioning ther brands). There
was a problem. Even though the heater load was within the timer's
stated load, the live pin on the plug used to get very warm. Not
enough to burn, but eventually th heat yellowed & distorted the
plastic in both the plug and the timer.

Maybe it's something like that.

W.