Write to your landlord and tell him politely that your heating system is defective. Stress the potential harm to your young child. Ask him to send a qualified person to investigate and rectify the problem. Tell him that if nothing happens after two weeks you will engage your own specialist and deduct the costs from your rent. Escessive heating is very probably costing you money.
He has an obligation to keep the systems in the property working properly and should make repairs in a reasonable time.
Speak to citizens advice; and get them to make a note of your conversation, to clarify the legal obligations of landlord and tenant.
The 30kW rating is nothing to do with how hot the water gets - just the potential for how much heat may be generated - you should still be able to adjust the water temperature if it were 100kW. Borrow or even buy a thermometer and measure the outlet temperature of the tap water - and the top of the radiators. Put the figures in your letter.
It very probably is the thermostat but that's not your concern - it's the landlord's problem.
He has no obligation (I think) to fit TRVs but you could offer to pay for them to be fitted if you envisage staying there for a long time. As a notional cost allow perhaps £20 - £25 per rad in total. It might spur him into action on the boiler problem.
Peccavi
October 2008