Losing battle I'm afraid!. You can't "put too much load on the boiler", it will just produce its output and that's it, it can't be "strained" by having to heat a large cold room!
You would need about 30,000 Btu rad in the conservatory to beat the cold in the winter. Best way is to have insulated blinds all round (and I mean insulated). We have these and they make a huge difference. If just one of the blinds is not down properly we can notice the difference. Unfortunately these cost serious money. A mate of mine recently had his done and saw no change from £5,000
However, increasing radiator size will help obviously but usually conservatories have very little wall area to allow big rads to be fitted.