How much does a radiator at 25˚C affect a room that is 20˚C? This is probably not a very precise question but I'm just trying to get a rough idea how much effect a radiator set at such a low temperature would have on a room. Let's assume that the number of radiators and size of the radiators is generally appropriate for the size of the room. Make up your own approximate values for these.
I want to get some idea whether it has some effect or is basically negligible in a real world application and if it does affect the room's temperature, how long would it take to do that.
 A: $25^{\circ}$ is of course a very low radiator temperature, $\approx 60^{\circ}$ being far more common.
But even at $25^{\circ}$ there's positive heat transfer going from the radiators to the room, as long as the room's temperature is below $25^{\circ}$)
Newton's Law of cooling/heating is very enlightening here:
$$\dot{Q}=hA\left(T(t)-T_{env}\right)\tag{1}$$
(Please consult the link above for precise meaning of symbols) For this question $T_{env}$ is the radiator temperature (assumed constant at $25^{\circ}$)
Firstly and intuitively it's clear that heat transfer $\dot{Q}$ (flux - radiator to room) is greatly influenced by $T(t)-T_{env}$, so that:
$$\dot{Q}\propto\left(T(t)-T_{env}\right)$$
Here the Law is written for cooling but it works equally well for heating.
Secondly, $(1)$ can be re-written as an ODE because:
$$\dot{Q}=-mC_p\frac{\mathrm{d}T(t)}{\mathrm{d}t}\tag{2}$$
where $m$ is the total mass of air in the room and $C_p$ the specific heat capacity of air.
Combining $(1)$ and $(2)$ we get, reworked:
$$-\frac{\mathrm{d}T(t)}{T(t)-T_{env}}=\frac{hA}{mC_p}\mathrm{d}t\tag{3}$$
Set $\alpha=\frac{hA}{mC_p}$, then:
$$-\frac{\mathrm{d}T(t)}{T(t)-T_{env}}=\alpha\mathrm{d}t\tag{4}$$
$(4)$ integrates to:
$$\ln\left[\frac{T_{end}-T_{env}}{T_{begin}-T_{env}}\right]=-\alpha t$$
which gives you the temperature evolution of $T_{begin}\to T_{end}$ (room). It also tells you which factors influence it and how. Given enough time ($t\to +\infty$) the toom temperature will equal the radiator temperature.
Note of course that this is a idealisation that relies on some factors, like $T_{env}$, to be constant.

I want to get some idea whether it has some effect or is basically
negligible in a real world application and if it does affect the
room's temperature, how long would it take to do that.

This will largely depend on factors like $h, A, m$ and $T_{env}$, as evidenced above.

$h\approx 20\mathrm{W/(m^2 K)}$
$A=3.6\mathrm{m^2}$
$VC_p=90750\mathrm{W/K}$
$\alpha=\frac{hA}{VC_p}=8\times 10^{-4}\mathrm{s^{-1}}$
Calculate time for room to reach $90$ percent of $25^{\circ}$, which  is $22.5^{\circ}$.
$\ln\left[\frac{T_{end}-T_{env}}{T_{begin}-T_{env}}\right]=\ln\left[\frac{22.5-25}{20-25}\right]=\ln 0.5$
$t=-\frac{\ln 0.5}{\alpha}=866\mathrm{s}=14\mathrm{min}$
A: If the temperature of the radiator is higher than the temperature of the room then there will be a flow of heat from the radiator to the room. The rate at which heat flows into the room will be proportional to the difference between the radiator temperature and the room temperature.
If the room is hermetically sealed and perfectly insulated then the temperature of the room and everything in it will increase until it reaches the same temperature as the radiator. The time that this takes (or, more exactly, the time it takes for the room temperature to get close to the radiator temperature, since exact equality will take an infinite length of time) will depend on many factors, including the size of the room, the size and material of the radiator, the contents of the room. This case is dealt with in detail in Gert's answer. Note that in no circumstances can the radiator heat the room to a temperature that is higher than the radiator temperature - this would violate the second law of thermodynamics.
However, in reality it is likely that the room will not be hermetically sealed and perfectly insulated, and the temperature of the outside environment is likely to be no higher than the room temperature. In this case, as the room temperature rises, there will be a flow of heat energy from the room to the outside environment. The steady state room temperature will now be the temperature at which the rate of heat flow from the room to the outside equals the rate of heat flow from the radiator into the room - this will be lower than the radiator temperature but greater than the outside temperature.
So the best we can say for a real room is that given enough time the radiator will heat the room to some temperature between $20^o$C and $25^o$C, depending upon how well sealed and insulated the room is.
