Modifyiing Derivative part in PID

So, I have a problem.. Maybe. I only had 3 test runs with the system so I'm not sure.
It is a steam cooling system, and I thought it would be easy. I need to keep the steam at 240 +/. 5°C.
The problem is the lag, especially in the start or the changeing of the blowers setpoint...

The temperature starts rising 1-2 °C per second.. So I would like the regulator to start even when the temp is 220 or so, just to slow it down, but if I set the D part so high(big), I'll have problems when I get near the setpoint...

So I was thinking about modifyiing the D part..

a) adaptive regulation, something like D part being stronger the further the PV is from the SP..
b) makeing it cumulative - so D = D_new + k*D_old

Of course, maybe on the 4th or 10th try, the normal PID will work..

But I wanted some opinions if it doesn't, maybe some of you had some experience with something like that, I rarely turn on the D part at all so..

If I try one of the ideas, what should I be careful of ..
Do you have any other ideas..
Are there any "standard" modifications..
Any advice will help to prepare me better..

(I have the filter on the D part, just to say..)

make a model of your system, then use the model to figure out what gains you should use.

I believe it is called gain scheduling when the gains change with the PV but this should only be required when the system has a different response at different PVs.