Slow warmup, when kettle reaches 450 and oil is added the temp drops down to about 350.

Just cooked a 15 pounder with stuffing wrapped tightly in foil on a rack in a roasting pan at 450 degrees 1/2 hour then dropped to 350 for 4 1/2 hours in a convection oven, the foil keeps the moisture in. Uncover last 1/2 hour for crispy skin

if it is an electronic timer temp controller you might want to check it

It sound like the temperature sensor that switches the kettle off when it has reached the correct temperature is faulty. It would probably be cheeper to replace than repair

Unfortunately, it's not realistically designed to heat above 250 -275 Degrees F. No matter what they call it, it's still a smoker, more than it is a grill. Even the Owner's Manual says the the optimal operation temperature is 180 to 200 degrees F. It's not designed to sear steaks.

Perhaps, if it was made of cast iron, rather than sheet steel, you could get the temp up past 350 degrees. If you really want a true smoker/grill, pay $700 to $800 and buy a Big Green Egg. And you wont have to buy some specialized pellets to burn in it. Just good old fashioned lump charcoal or wood chunks.

I wish I had better news for you, but it is what it is. Thanks for choosing FixYa.

Oil temperature normally drops when product is loaded especially chilled or frozen products. Oil temperature should reach the set point before cooking time ends.

Check any bypass hoses that are around the engine for blockage or internal swelling. If the bypass hoses are restricted, warmup time will be extended. Even though the thermostat is new, the valve may still not be seating properly when closed and allowing some flow when engine is still cold and slowing warmup. Check by shining torch at thermostat valve seat to see if there any gaps. Most thermostats also have a little tickle valve in the outside rim, that is held closed by the water pump pressure but allow a trickle flow when engine is stopped for cool down. If this valve is missing or sticking, that will also slow the warmup process.

If you are monitoring the oven temperature with an analog style thermometer you may actually be ok, but seeing the thermometers slow reaction time.
Some newer ovens actually do pre-heat beep prior to reaching temp in an effort to conserve eelectricity.
A good home test is to try your oven at several different temps to see if there is any variation in internal temperature. Try it one day on 300, the next at 375 and another day at 450. Give your analog style thermometer time to catch up (usually just about 15 min) and leave it on for a half an hour to see if the temp maintains.
Also Beware of aluminum foil AND THE NEW OVEN LINER MATS as they can alter oven performance bay absorbing and blocking the ovens natural heat radiation and convection air flow currents that happen in all ovens, not just convection models.
Another interesting fact is that older ovens used a thermostat in them that operated much like your thermometer and was very slow to react making the oven typically about 100 degrees hotter than where the customer set it. This was just a fact of life before the advent of electronic temperature management and became noticeable when people began trying to bake older "hand me down" recipes in the newer ovens with less than stellar results.
You can mimic the older oven performance by preheating the oven about a hundred degrees higher than called for and after it reaches temp, re-set it to the correct temperature and put the items in right away.
If you find your temperatures fluctuating ask your servicer to replace first the temp sensor and as a last resort the control board as this part is usually pretty expensive.
Good Luck with this!

Set the thermostat to 350 degrees,get a thermometer and put it in the oil,when the unit shuts off look at the temp of the oil.If the temp of the oil is higher then the thermostat is bad if not the hi-limit may be.Let me know.

a faulty bake ignitor would not allow the unit to maintan temp , very common issue with all gas ranges

how do you know it is dropping 100 degrees ?
If the set temperature is 350-400 the heaters will work untill the thermostat will read that the temperature is reached - after that the heaters will shut down and the temperature will drop...and after few minutes when the temperature goes below thw set point (in this case 350-400) the heaters will turn on again - this will happen for the duration of the timing you have selected (example 45 minutes)