Heating a conservatory?

[BumpPlus2]

Hi,
We have a conservatory used as a playroom off the kitchen, as with most conservatories (I am led to believe) it is colder than a cold thing and often more akin to a fridge
We had an electric heater on the wall when we moved to this house but that has since broken and we were making do with a fan heater plugged in through the kitchen and into the playroom...
Problems - can't shut the playroom door to keep the heat in, cold out. Also heater is not the safest for visiting DC's as is very tempting for them to stick things in it and have to watch like hawk (my DS's are used to it now and steer clear)
Any advice please of best way to heat this room? My DS's are all 4 and under and it needs to be as childsafe as possible as one is only a baby so will be using that room for years to come.
Thanks so much

No answer on the actual heating, but thought I'd ask what you have down on the floor. We have those thick foam play mats (got ones that are actually for industrial use at Costco as they were cheaper than the kids version). I find it makes the floor much warmer than a rug, and quite comfy for them to play on.

Will keep an eye for others heating suggestions.

We have a very large central heating radiator in ours and it is still freezing! If I was building a conservatory I would build a 'garden room' instead, i.e. a conservatory with a proper solid insulated roof. Some on MN have investigated retrofitting an insulated ceiling or roof, which apparently makes a huge difference. I am putting up with ours until we knock it down and replace it with a proper extension.

As for heaters, have you seen this current MN competition? Or a similar oil filled electric radiator would do the same thing.

We have underfloor heating, it is on a timer, has kept it warm enough to use and have the doors open even with snow outside. I think it was about £500 to buy and install, but obviously you would need new flooring laid over it too. It is also expensive to run, but for me it is worth it for the extra space it creates.

Ahhhh thanks guys!
We have a tiled floor overlaid with thick foam playmats - snap - RunsWithScissors.
I don't think we are looking to spend much on the heating as eventually this conservatory will come down and become an extension...if we stay at this property long enough - just need a heating solution until April when the room becomes to hot!!!!
We are debating a 'proper' conservatory (the one we have came with the house when we bought it and is very cheaply constructed) so will be taking a lot of your suggestions for that one - ie u/f heating

FannyPriceless - entered! Thank you

Doesn't help your current problem but I would go for a 'proper' extension rather than a 'proper' conservatory if I were you. We moved into a house with an expensive bespoke conservatory. It is still freezing in winter and boiling in summer and a total waste of space imo.

pootlebug thanks for that - it's a big quandry and interesting when you say you have the Rolls Royce version so to speak and it's still got those age old issues

When DC in conservatory in the autumn/winter/spring (!) we put an oil filled radiator in - it cost about £90.

We are getting rid of conservatory - seems colder than outside at times and in the summer it is so bright you need to wear sunglasses. We're looking at getting an extension for a garden room and quoted £2,000 per square metre.

We also use an oil filled radiator - £70 from John Lewis.

I hate ours, but came with the house when we bought it.