I’m going to have to call the appliance repair guy (as soon as I figure out who) but I thought I’d throw it out to you good people first. Just for ideas.
It’s a twelve year old stove that really hasn’t given us any trouble. But now when we turn the oven on it can take forever to preheat, depending on the temperature. If it’s under 350 it works about like it always has, but if it’s over that it takes sometimes more than an hour just to preheat. I don’t have an oven thermometer, so I’ve wondered if it’s actually getting to temperature but not registering, so it doesn’t set off the beeper.
Then there’s the fact that sometimes when it’s heating it smells almost like plastic. Not gas. I recognize the smell of gas. This is more chemical or ‘artificial’ if that makes any sense.
So what do you think? Thermostat? Is there anything I should be checking, just to see if it’s a simple fix?
From your description - if it is a gas oven, call in a pro. Repairing a gas oven, is dangerous, can void your insurance’, even if the fire can not be linked to the stove, oh and kill you.
Your gas company may have a toll free tips advice line you can call. Also the manufacturer will probably have a web site. Just type the make, model and product number and a brief description of your problem and several websites willl come up.
If it is electric, it sounds like one of the two heating elements is not working. The second element is used to achieve higher temperatures. If you turn on the broiler with the oven you should be able to see two elements glowing. If you only see one, that’s the problem.
Google appliance repair sites to confirm this diagnosis and even purchase a part online to save money.
It’s a gas stove, with electric ignition, or whatever they call that. No pilot lights. My husband keeps insisting it might need cleaning, but I can’t figure out how that would have this effect, and we haven’t had anything spill in it or make a mess, not even little ones. I plan to call somebody to fix it. I’m just mostly wondering if I’ve missed anything little and silly.
The cleaning would be my only advice - inside the oven cavity there will be, in a top corner a metal rod (the oven temp sensor/thrmostat) close to the roof. If it becomes dirty, or bent too far away from the wall, they symptoms you describe could be occurring. It shoul;d be no more than an inch away from the wall at its tip.
Have a look there. other than that time to call in a professional
best of luck
I learned far too much about how those types of ovens work when we had a similar problem. It sounds very like the “glow ignitor” in your oven has aged to a point where it isn’t triggering the gas to come on at all.
Scroll down to “Hot Surface (‘Glow Bar’) Ignition System,” which as noted is the most common system.
I ordered the new glow ignitor and my husband had it installed in less than 30 minutes. I was going to do it myself – the instructions were straightforward and it was simple – but I believe a manhood issue was at stake. 
You could also just call out a repair service, but for us, it was the difference between a couple of hundred dollars and less than $25. I just looked up the make and model of our stove and ordered the part online. Easy-peasy.
Edit to add - replacing this part doesn’t involve the gas line in any way. On our model of stove, the part literally had a plug-type connector. We just unplugged the old one and plugged in the new. Obviously the stove was disconnected from the electrical wall outlet during this.
Cleaning may help. It if the gas orifices get dirty the flame doesn’t generate as much heat. Also it could be the thermocouple or the temperature control, but you seem to think it never gets hot enough, so a dirty or corroded burner sounds more likely.
But this is not great advice. I’m used to commercial kitchen gas appliances which are often simpler than the household versions.